Refereed Research Publications in Journals:

• 1. "On Green's Functions of an n-point Boundary Value Problem," Transactions of the AMS, Vol. 182 (1973) 469-480 (with K. M. Das).
• 2. "Green's Functions for an n-n Boundary Value Problem and an Analogue of Hartman's Result," Journal of Mathematical Analysis and Applications, Vol. 51 (1975) 670-677 (with K. M. Das).
• 3. "Existence and Comparison Results for a Class of Volterra Integral Equations of Sobolev Type," Journal of Integral Equations, Vol.1(1979) 183-191 (with V. Lakshmikantham and R. L. Vaughn).
• 4. "Existence and Comparison Results for Differential Equations of Sobolev Type," Applied Mathematics and Computation, Vol. 6 (1980) 177-187 (with R. L. Vaughn).
• 5. "Existence of Extremal Solutions and Comparison Results for Delay Differential Equations in Abstract Cones," Rendi Conti del Seminario Mathematica di Padova, Vol. 64 (1980) 1-14 (with R. L. Vaughn).
• 6. "Quasi Solutions and Monotone Method for Systems of Nonlinear Boundary Value Problems," Journal of Mathematical Analysis and Applications, Vol. 79 (1981) 38-47 (with V. Lakshmikantham).
• 7. "Comparison Results of Reaction Diffusion Equations with Delay in Abstract Cones," Rendi Conti del Seminario Mathematica di Padova, Vol. 65 (1981) 19-34 (with Shair Ahmad).
• 8. "Stability Results for Solutions of Reaction Diffusion Equations by the Method of Quasi-Solutions," Applicable Analysis, Vol. 12 (1981) 229-235 (with V. Lakshmikantham).
• 9. "Method of Quasi-Upper and Lower Solutions in Abstract Cones," Nonlinear Analysis, Vol. 6 (1982) 833-838 (with V. Lakshmikantham and S. Leela).
• 10. "Monotone Method for Equations Describing Transport Phenomena in a Banach Space," Applied Mathematics and Computation, Vol. 9 (1981) 165- 174 (with B. G. Pachpatte).
• 11. "Comparison Results for First and Second Order Boundary Value Problems and Resonance," Applied Mathematics and Computation, Vol. 12 (1983) 267-380 (with G. R. Shendge).
• 12. "On the Existence of Periodic Quasi-Solutions for First Order Systems", Nonlinear Analysis," Vol. 7 (1983) 1283-1289.
• 13. "Comparison Results for Parabolic Boundary Value Problems at Resonance," Applied Mathematics and Computation, Vol. 15 (1984) 209-222 (with G. R. Shendge).
• 14. "Monotone Iterative Technique for Partial Differential Equations of First Order," Journal of Mathematical Analysis and Applications Vol 102 (1984) 393-398 (with V. Lakshmikantham and M. N. Oguztorelli).
• 15. "Existence of Solution for a System of Second Order Nonlinear Periodic Boundary value Problem,l" Applicable Analysis, Vol. 17 (1983) 23-36 (with V. Sree Hari Rao).
• 16. "Monotone Method for a System of Second Order Periodic Boundary Value Problems," Applied Mathematics and Computation, Vol. 15 (1984) 71-84 (with V. Lakshmikantham and V. Sree Hari Rao).
• 17. "Existence of Coupled Quasi-Solutions of Systems of Nonlinear Elliptic Boundary Value Problems," Nonlinear Analysis, Vol. 8 (1984) 501-515 (with G. S. Ladde and V. Lakshmikantham).
• 18. "Existence of Coupled Quasi-Solutions of Systems of Nonlinear Reaction Diffusion Equations," Journal of Mathematical Analysis and Application," Vol. 108, No. 1, May 15, 1985 (with G. S. Ladde and V. Lakshmikantham).
• 19. "Monotone Method for Integrodifferential Equations with Periodic Boundary Conditions," Applicable Analysis, Vol. 121, No. 4 (1986) 297-305 (with S. K. Kaul).
• 20. "Periodic Boundary Value Problem for First Order Partial Differential Equations," Applicable Analysis, Vol. 20 (1985) 107-115.
• 21. "Method of Mixed Monotony for Nonlinear Equations with a Singular Linear Part," Applied Mathematics and computation, Vol. 23 (1987) 235-241 (with V. Lakshmikantham).
• 22. "Monotone Technique for First Order Periodic Boundary Value Problem in a Banach Space," Applicable Analysis, Vol. 23 (1987) 277-285 (with S. W. Du).
• 23. "Method of Upper and Lower Solutions and Interval Method for Semilinear Euler-Poisson-Darboux Equations," Journal of Mathematical Analysis and Applications (1990), 378-384, (with C. Y. Chan).
• 24. "Monotone Method for First Order Singular Systems with Boundary Conditions," Journal of Applied Mathematics and Simulation (1989), 217-224 (with J. A. Uvah).
• 25. "Monotone Iterative Technique for Nonlinear Boundary-Value Problem of First Order differential Systems with Rectangular Coefficients," Journal of mathematical Analysis and Applications (1991), 482- 493 (with J. A. Uvah).
• 26. "Periodic Boundary Value Problems of Impulsive Differential Equations," Applicable Analysis (1992), pp. 145-158 (jointly with Yong Sun).
• 27. "Monotone Iterative Technique for Nonlinear IVP of Integrodifferential Systems with Singular Coefficients," Applicable Analysis, Vol. 51 (1993), 129-138 ) jointly with J. A. Uvah.
• 28. "Impulsive Quenching for Reaction Diffusion Equations," (with C. Y. Chan and Lan Ke) Nonlinear Analysis, Vol. 22, No. 11, pp 1323-1328, 1994.
• 29. "Global Results via Perturbing Lyapunov Functions," (jointly with S. Leela and S. G. Rajalakshmi) Dynamic Systems and Applications, 3 (1994) 113-120.
• 30. "The Method of Generalized Quasilinerization in Finite Systems," Nonlinear World 3 (1996), pp151-157.
• 31. "Method of Generalized Quasilinearization for Second Order Boundary Value Problem," Commemorative Volume dedicated to Professor Wolfgang Walter, Inequalities And Applications, (1994), pp449-457, World Scientific .
• 32. "Improved Generalized Quasilinearization Method for Second Order Boundary Value Problem," (with N. Shahzad) Dynamic Systems and Applications, 4, 79 - 86,(1995).
• 33. "Composite Boundedness and Stability Results by Perturbing Lyapunov Functions," (with Donna Stutson), Nonlinear Analysis, V 26, No. 4, pp.761-766, (1996).
• 34. "Extension of the Method of Generalized Quasilinarization for Second Order Boundary Value Problem,"(with N. Shahzad), Applicable Analysis, Vol. 58, 77-83, (1995).
• 35. "Generalized Quasilinearization and Reaction Diffusion Equations," Nonlinear Times and Digest, Vol. 1, No. 2, pp 211- 220, 1994.
• 36. "Monotone Iterative Technique for a system of First Order Functional Partial Differential Equations," (with Drumi Bainov and Emil Minchev), Journal of Nonlinear Differential Equations: Theory, Methods and Applications, Vol. 1, 111-125, (1995).
• 37. "Reaction Diffusion Equations and Quadratic Convergence," (with H. Alkhaby and M. Mahrous) Journal of Applied Math and Stochastic Analysis, Vol. 10:2, pp 179-186, (1997).
• 38. "Quadratic and Semi-Quadratic Convergence of IVP," (with Donna Stutson), Neural, parallel and Scientific Computation, Vol. 3, pp235-248, (1995).
• 39. "Stability of Moving Invariant Sets," (with V. Lakshmikantham) Advances in Nonlinear Dynamics, 79-83, Gordon & Breach Science Publishers, Stability and Control: Theory, Methods & Appl. V 5, 1997.
• 40. "Generalized Quasilinearization and First Order Periodic Boundary Value Problem," (with D. Stutson) Applied Math and Computation, 77:113-129, (1996).
• 41. "Generalized Practical Stability Results by Perturbing Lyapunov Functions," (with D. Stutson), Journal of Applied Math and Stochastic Analysis, Vol. 9. No 1, 69-75, (1996).
• 42. "Generalized Quasilinearization for Impulsive Differential Equations with Fixed Moments of Impulse," (with J. Vasundara Devi and G. Chandrakala) Dynamics of Continuous, Discrete and Impulsive Systems, 1, 91-99, (1995).
• 43. "Dynamic Systems on Time Scales and Generalized Qasilinearization," (Jointly with S. Leela) Nonlinear Studies, Vol. 3, No 2, 179-186, (1996).
• 44. "Stability of Moving Invariant Sets for Functional Differential Systems" (Jointly with S. G. Deo) International Journal of Nonlinear Differential Equations, Theory, Methods and Applications V 3, No 1& 2, 179-186 (1997).
• 45. "Strict Stability Criteria for Dynamic Systems on Time Scales" Journal of Difference Equations and Applications V3, 267-276 (1998).
• 46. "The Present State of UAS for Voltera and Delay Equations ( with V. Lakshmikantham), special issue dedicated to Professor Volterra, (1999) 83-93, in Gordon Breach Science Publishers.
• 47. "Second Method of Lyapunov for Stability of Linear Impulsive Differential-Difference Equations with Variable Impulsive Perturbations" ( with D.D. Bainov and I. M. Stamova) Journal of Applied Math and Stochastic Analysis V11, No 2, pp. 209-216, (1998).
• 48. "Global Stability of Sets for Linear Impulsive Differential-Difference Equations with Variable Impulsive Perturbations" (with D.D. Bainov and I. M. Stamova), Applicable Analysis, Vol. 62, pp 149 - 160, (1996).
• 49. "Variation of Parameters in Terms of Lyapunov-like Functions and Stability of Perturbed Systems" (with Xinzhi Liu), Nonlinear Studies, V 5, Number 1 pp. 47-58, (1998).
• 50. "Generalized Quasilinearization Method for First Order Periodic Boundary Value Problem with Fixed Moments of Impulse" (with Shobha Rani and Vasundhara Devi), Communications in Applied Analysis. V 3, pp 517-527, (1999).
• 51. "Generalized Quasilinearization for Impulsive Reaction-Diffusion Equations with Fixed Moments of Impulses" (with Zahia Drici and Nader Kouhestani), Dynamic Systems and Applications , Vol. 7, No 2, pp. 245-257, (1998).
• 52. "Generalized Quasilinearization for Systems of Reaction-Diffusion Equations" (with Jiang Jiahui), Applied Math and Computation Vol. 97, pp. 223-235 (1998).
• 53. "An Extension of Quasilinearization to Reaction Diffusion Equations with Fixed Moments of Impulses" (jointly wit Zahia Drici and Nader Kouhestani) Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 7, 33-50, (2000).
• 54."Large Delay Differential Equations and Variational Lyapunov Method," (Jointly with Sonya Felton) International Journal, "Problems of Nonlinear Analysis in Engineering Systems", Vol. 2, No 8, pp. 42- 48, (1998).
• 55. "Differential Inequalities with Initial Time Difference and Applications" (jointly with V. Lakshmikantham) "Journal of Inequalities and Applications", Vol 3, pp. 233-244, (1999).
• 56. "Theory of Differential and Integral Inequalities with Initial Time Difference and Applications" (jointly with V. Lakshmikantham) pp. 191-203 "Analytic and Geometric Inequalities and Applications" Kluwer Academic Publishers, (1999).
• 57. "The Origin of Mathematics," (jointly with V. Lakshmikantham) Nonlinear Studies, Vol. 5, Number 2 pp. 255-257, (1998).
• 58. "The Method of Generalized Quasilinearization and Its Applications," (jointly with V. Lakshmikantham) Neural, Parallel and Scientific Computation, V. 7, No. 2, pp. 119-140, (1999).
• 59. "Method of Generalized Quasilinearization for Reaction Diffusion Equations in Unbounded Domains" (Jointly with Liwen Wang) JMAA, 237, pp. 645-656, (1999).
• 60. "Existence of Fixed Points of Fuzzy Mappings Via Theory of Fuzzy Differential Equations" (jointly with V. Lakshmikantham) Journal of Computational and Applied Mathematics 113, 195-200, (2000).
• 61. "Convex Dependence of Solutions of Nonlinear Parabolic Equations Relative to Initial and Boundary Values," (Jointly with Xiaoquan Zhao) Journal of Nonlinear Differential Equations, Theory, Methods & Applications, Vol 5 Nos 1 and 2, pp. 76-79, (1999).
• 62. "Monotone Flows and Mixed Monotone Reaction Diffusion Systems," (Jointly with V. Lakshmikantham) Volume dedicated to Professor Corduneanu’s 70th birthday in 1998, ANALELE STINTIFICE ALE UNIVERSITATH "AL.1.CUZA" IASI Tomul XLIV, s.I a, Mathematica, pp 263-269 [Printed in 2000]
• 63. "Generalized Quasilinearization Method for Parabolic Integro-differential Equations," (jointly with Liwen Wang) Quarterly of Applied Mathematics, Volume LIX, Number 3, pp 459 –470, Sept 2001.
• 64. "Extended Method of Quasilinearization for Systems of Nonlinear Differential Equations," (Jointly with K. Vajravelu, Applicable Analysis, 74(3-4) pp. 333-349, 2000.
• 65. "Quasilinearization Method for Second Order Singular Boundary Value Problems with Solutions in Weighted Spaces" [jointly with J. Vasundhara Devi] Journal of Korean Mathematical Society, Vol. 37, No. 5, pp. 823-833, September 2000.
• 66. "Method of Quasilinearization for the Periodic Boundary Value Problem for Differential-Difference Equation", [Jointly with S. G. Hristova] Dynamic Systems and Applications, Vol. 9, Number 4, pp. 515-526 [2000]
• 67. "Some Results on Reaction Diffusion Equations with Initial Time Difference", Volume dedicated to Professor V. Laksmikantham’s 75th birthday, Differential Equations and Nonlinear Mechanics, pp 391- 400, Kluwer Academic Publishers, Ed. K. Vajravelu, 2001.
• 68. "Generalized Quasilinearization and Semilinear Elliptic Boundary Value Problems", [Jointly with V. Lakshmikantham] volume dedicated to 80th birth anniversary of Richard Bellman, JMAA, 249, 199- 220. 2000.
• 69. "Generalized Quasilinearization Method for Reaction Diffusion Equation with Periodic Conditions", [Jointly with T. Gnana Bhaskar], Problems of Nonlinear Analysis in Engineering System, 7, pp. 38- 46, 2001.
• 70. "Monotone-Iterative Techniques for Impulsive Hybrid Systems with Variable Moments " [Jointly with S. G. Hristov] International Journal of Hybrid Systems , Vol 1, No 1, pp 79 –90, 2001.
• 71. "Rapid Convergence of the Iterative Technique for Reaction Diffusion Equations," submitted.
• 72. "Hybrid Systemson on Time Scales,"[Jointly with V. Lakshmikantham] "Journal of Computational and Applied Mathematics"[Special issue] 141 (1-2) 1-284, (2002).
• 73. "A unified Exhaustive Study of Monotone Iterative Technique for Initial Value Problems," (Jointly with Michael Sokol) to Nonlinear Studies, Vol. 8, No 4, 2001.
• 74. "Basic Theory of Fuzzy Difference Equations," [Jointly with V. Lakshmikantham] Issue Dedicated to Professor Allan Peterson’s 60th birthday, " Journal of Difference Equations and Applications, V 8, 978-989, (2002).
• 75. "Generalized Monotone Technique for an Impulsive Differential Equation with Variable Moments of Impulse", [Jointly with J. Vasundhara Devi], Nonlinear Studies, Vol. 9, No. 3, pp 319-330, 2002.
• 76. "Setvalued Hybrid Differential Equations and Stability in Terms of Two Measures", [Jointly with V. Lakshmikantham and S. Leela], International Journal of Hybrid Systems , Vol 2, Nos 1 & 2, 169-187, 2002.
• 77. "Generalized Quasilinearization for Impulsive Differential Equations with Variable Moments of Impulses", [Jointly with J. Vasundhara Devi] Dynamic Systems and Applications, V12, pp 369-382, 2003.
• 78. "Interconnection Between Set and Fuzzy Differential Equations", [Jointly with V. Lakshmikantham and S. Leela] Nonlinear Analysis, 54 (2003) 351-360.
• 79. "Set Differential Equations and Monotone Flows" [Jointly with V. Lakshmikantham] "Nonlinear Dynamics and Systems Theory", 3(2) (2003) 151-161.
• 80. "Generalized Quasilinearization Versus Newton's Method", [Jointlywith V. Lakshmikantham], Applied Math and Computation" the special issue "12th International Workshop on Dynamics and Control", 164, pp 523-530, 2005.
• 81. "Impulsive Hybrid Fuzzy Differential Equations" Univesity of NIŠ, Facta Universitatis, Series Mechanics, Automatic Control and Robotics, Vol3, No 14, (2003) 851-858.
• 82. "Generalized Monotone Iterative Method For Initial Value Problems", [Jointly with Ianna H, West] Applied Mathematics Letter Vol17, No 11, 1231-1237,2004.
• 83. "A study of Set Differential Equations with Delay" [ Jointly with J. Vasudharada Devi] Special issue of "Dynamics of Continuous, Discrete and Impulsive Systems", Series A: A Mathematical Analysis 11 (2004) 287-300.
• 84. "Hybrid Impulsive Fuzzy Differential Systems" [Jointly with V. Lakshmikantham] "International Journal of Hybrid Systems" V3, No 1, (2003) pp 85-93.
• 85. Method of Vector Lyapunov Functions for Impulsive Fuzzy Systems, Special issue of Dynamic Systems and Applications, V 13, No 4, pp 521-532, 2004.
• 86. Generalized Quasilinearization Method for Reaction Diffusion Systems [Jointly with Jie Yang] Nonlinear Studies, V 13 Number 1, pp 53-72, 2006.
• 87. Monotone Iterative Technique for Impulsive Set Differential Equations, [Jointly with J. Vasundhara Devi] Nonlinear Studies, Vol 11, No 4, pp 639-658, (2004).
• 88. Generalized Monotone Method for Second Order Boundary Value Problems, [Jointly with Ianna H, West].Neural, Parallel and Scientific Computation , V13, No 2, 213-227, 2005.
• 89. Generalized Quasilinearization method and Higher Order of Convergence for First Order Initial Value Problems, [jointly with Tanya Melton], Dynamic Systems and Applications(15) 2006, 375-394
• 90. Numerical Approach for the Solution of Reaction Diffusion Systems via Generalized Quasilinearization Method, [jointly with Jie Yang]. Computers and Mathematics with Applications, pp 587-598, 50 (2005).
• 91. Monotone Iterative Technique for Semi-linear Elliptic Systems [Jointly with J. Yang ] Boundary Value Problems 2, pp 93- 106, 20005, Hindawi Publishing Corp
• 92. Development of the Method of Generalized Quasilinearization, Bulletin of the Marathwada Mathematical Society 2004.
• 93. Numerical Applications of Generalized Quasilinearization Method and Rapid Convergence, [Jointly with Tanya Melton] Neural, Parallel and Scientific Computation V 12, No 4 pp 567-576, 2004.
• 94. Stability in Terms of Two Measures of Hybrid Systems with Partially Visible Solutions, Jointly with V.Lakshmikantham, J. Vasundhara Devi, Nonlinear Analysis TMA special issue Hybrid Systems and Applications (1), Vol 62 No 8, 1536-1543, 2005.
• 94. Improved Generalized Method and Rapid Convergence for Reaction Diffusion Equations, [Jointly with Tanya Melton] Applied Math and Computation,203,(2008), 563-572.
• 95. Quasilinearization for Periodic Boundary Value Problem for Systems of Impulsive differential Equations, [with S. G. Hristova] JAMSA, Volume 2006 (2006), Article ID 98318,25 pages, Hindawi
• 96. Generalized Quasilinearization Method and Higher Order of Convergence for Second Order Boundary Value Problems, (with Tanya G. Melton ), Boundary Value Problems, 2006, Article ID 25715, 15 pages , Hindawi.
• 97. Generalized Monotone Iterative Technique for Functional Differential Equations with Retardation and Anticipation, Nonlinear Dynamics and Systems Theory, 7(4) 2007 pp 431-438.
• 98. Generalized Monotone Iterative Method for Integro-Differential Equations with Periodic Boundary Conditions, (with Ianna H. West) Mathematical Inequalities and Applications, V 10, No 1, pp 151- 163, 2007.
• 99. Generalized Quasilinearization Method and Cubic Convergence for Integro-Differential Equations (with Tanya G. Melton), accepted to Journal Qualitative Theory of Differential Equations and Applications, V 2, No 2, pp 154-169, (2008)
• 100. Theory of Fractional Differential Inequalities and Applications, with ( V. Lakshmikantham) Communication in Applied Analysis 11 (2007) 395-402.
• 101. Higher Order of Convergence via Generalized Quasilinearization Method for Parabolic Integro-Differential Equations (with Tanya Melton) Communication in Applied Analysis 11 (2007),403- 418.
• 102. Basic Theory of Fractional Differential Equations, with ( V. Lakshmikantham) Nonlinear Analysis, 69 (2008), 3837- 3343.
• 103. General Uniqueness and Monotone Iterative Technique for Fractional Differential Equations, (with V. Lakshmikantham) Applied Mathematics Letter (828-834), 2008.
• 104. Inverse Problems for Coefficient Identification for Euler Benoulii equation, (Jointly with Tchavder Marinov ) Computers and Mathematics with Applications) 56, (2008) pp 400-410.
• 105. Invariant Imbedding and Generalized Quasilinearization: A brief survey, (book Chapter, Advances in Theory, Methods and Applications in Dynamics and Control, V 4 Chapter 29, PP 323-327) Cambridge University Press series, (2009).
• 106. Generalized Monotone Method for Fractional Differential Equations with Applications, (Advances in Theory, Methods and Applications in Dynamics and Control, V 3, Chapter 16, PP 105-206) Cambridge University Press series, (2009.)
• 107. Generalized Montone Iterative Method for Impulsive Differential Systems (Jointly with Ianna West) Communications in Applied Analysis, 14, No 4, 301-310, 2010.
• 108. Fractional Integral Inequalities and Applications, (With Zach Denton), Computers and Mathematics with Applications, 59 , pp 1087-1094, 2010.
• 109. Monotone Iterative Technique for Fractional Differential Equations with Periodic Boundary Conditions, (Jointly with Diego Ramirez) Opuscula Mathematica, V. 29, No 3,pp 289-304, 2009.
• 110. Monotone Method for Nonlinear Caputo Fractional Boundary Value Problem", (with Diego Ramirez) Dynamic Systems and Applications 20 (2011) 73-88.
• 111. Monotone Iterative Technique for Finite Systems of Nonlinear Riemann Lioville Fractional Differential Equations, (jointly with Zach Denton), Opuscula Mathematica ,Vol. 31, No. 3, 2011, 327-339.
• 112. Quasilinearization Method Via Lower and Upper Solutions for Riemann-Liouville Fractional Differential Equations (jointly with Z. Denton and P.W. Ng) "Nonlinear Dynamics and Systems Theory, 11 (3) (2011), 239-251.
• 113. Generalized Monotone Method for Caputo Fractional Differential Systems via coupled lower and Upper Solutions, (with Donna Stutson), Dynamic Systems and Applications 20 (2011) 495-504.
• 114. Generalized Monotone Iterative Technique for Caputo Fractional Differential Equation with Periodic Boundary Condition via Initial Value Problem, with J. D. Ramirez International Journal of Differential Equations,Volume 2012 (2012), Article ID 842813, 17 pages, doi:10.1155/2012/842813, Research Article.
• 115. Generalized Monotone Method for Fractional Reaction Diffusion Equations, (with Stutson), Communications in Applied Analysis 16 (2012), no. 2, 165-174.
• 116. Existence of solution for impulsive hybrid differential equation, with B. M, Adams, N. Davis. Paige Epps, F. Miller, DeAndrai Mullen, Mathematical Sciences 2012, 6:19 doi:10.1186/2251-7456-6-19.
• 117. Generalized quasilinearization method for RL fractional differential equations, with Z. Denton, NONLINEAR STUDIES - www.nonlinearstudies.com, Vol. 19, No. 4, pp. 637-652, 2012.
• 118. Numerical Application of Generalized Monotone Method for Population Models, with C. Noel, H. Shiela, N. Zenia, P. Dayonna, W. Jasmine, and M. Sowmya, Neural, Parallel, and Scientific Computations 20 (2012) 359-372.
• 119. Generalized Monotone Method for Caputo Fractional Differential Equation with Applications to Population Models, (jointly with D. Ramirez and Th.T. Pham) Neural, Parallel and Scientific Computations 20 (2012) 119-132.
• 120. Sowmya Muniswamy and A.S. Vatsala Numerical Approach Via Generalized Monotone Method for Scalar Caputo Fractional Differential Equations, Neural, Parallel, and Scientific Computations 21 (2013) 19-30.
• 121. Sowmya Muniswamy and A.S. Vatsala Superlinear Convergence for Caputo Fractional Differential Equations with Applications, Dynamic Systems and Applications 22 (2013) 479-492.
• 122. An Amazing Legacy: a brief survey of the collected works of V.Lakshmikantham (08.08.1926- 06.07.2012). with S. Leela, International IFNA-ANS scientific Journal "Problems of nonlinear analysis in engineering systems", No.1(39), V.19, 2013, 120 - 140.
• 123. D. Stutson., and A.S.Vatsala Sub Hyperbolic Linear Partial Fractional Differential Equation in One Dimensional Space with Numerical Results Nonlinear Studies (special issue on fractional differential equations). NS Vol 20, No 4, 2013, pages 483-492.
• 124. Sowmya Muniswamy and A.S. Vatsala, Numerical Approach via Generalized Monotone Method for System of Caputo Fractional Differential Equations Neural, Parallel, and Scientific Computations 21 (2013) 347-360.
• 125. Vinchencia Anderson, Courtney Bettis, Shala Brown, Jacqkis Davis, Naeem Tull- walker, Vinodh Chellamuthu and Aghalaya S. Vatsala, Superlinear convergence via mixed generalized quasilinearization method and generalized monotone method, (2014) V 7, no.5, pp 699-712. INVOLVE : (2014) dx.doi.org/10.2140/involve.2014..101.
• 126. Donna S. Stutson and Aghalaya S. Vatsala., Riemann Liouville and Caputo Fractional Differential and Integral Inequalities, Dynamic Systems and Applications 23 (2014) 723-734.
• 127. D. Stutson., and A.S.Vatsala., Super Hyperbolic Linear Partial Fractional Differential Equation in One Dimensional Space, Communications in Applied Analysis, 18 (2014), no. 18, 401–408.
• 128. Amit Setia, Yucheng Liu, A.S. Vatsala, Numerical Solution off Fredholm-Volterra Fractional Integro-Differential Equationa with Nonlocal Boundary Conditions, Journal of Fractional Calculus and Applications, Vol. 5(2) July 2014, pp. 155-165. ISSN: 2090-5858.http://fcag- egypt.com/Journals/JFCA/.
• 129. Sowmya Muniswamy and A.S. Vatsala, Generalized Iterative Methods for Caputo Fractional Differential Equations via Coupled Lower and Upper Solutions with Superlinear Convergence, Nonlinear Dynamics and Systems Theory, 15 (2) (2015) 198–208.
• 130. Bhuvaneswari Sambandham and Aghalaya S. Vatsala, Basic Results for Sequential Caputo Fractional Differential Equations, Mathematics, 2015, 3, 76-91; doi:10.3390/math3010076 (mathematics ISSN 2227390,www.mdpi.com/journal/mathematics) .
• 131. M. Sowmya and A.S. Vatsala, Generalized Iterative Methods for Caputo FractionalDifferential Equations via Coupled Lower and Upper Solutions with Superlinear Convergence, Nonlinear Dynamics and Systems Theory, 15 (2) (2015) 198–208. CESS
• 132. Tchavdar T. Marinov, Rossitza S. MARINOVA, and Aghalaya S. Vatsala, Coefficient Identification in Euler- Bernoulli Equation from Over-posed Data, Neural, Parallel, and Scientific Computations, 23 (2015) 193-218.
• 133. J. Diego Ram´irez and Aghalaya S. Vatsala, Generalized Monotone Iterative Techniques for Caputo Fractional Integro-Differential Equations with Initial Condition, Neural, Parallel, and Scientific Computations, 23 (2015) 219- 238.
• 134. Bhuvaneswari Sambandham and Aghalaya S. Vatsala, Numerical Results for Linear Caputo Fractional Differential Equations with Variable Coefficients and Applications, Neural, Parallel, and Scientific Computations, 23 (2015) 253- 266.
• 135. Amit Setia, Bijil Prakash , and A. S. Vatsala, Numerical Solution by Fourth Order Fractional Integro-Differential Equation by Using Legendre Wavelets, Neural, Parallel, and Scientific Computations, 23 (2015) 377-386.
• 136. Aghalaya S. Vatsala, M. Sowmya, and Donna S. Stutson, Generalized Monotone Method for Ordinary Caputo Fractional Differential Equations, Dynamic Systems and Applications, 24 (2015) 429-438.
• 137. Aghalaya S. Vatsala and Bhuvaneswari Sambandham, Laplace Transform Method for Sequential Caputo Fractional Differential Equations, MATHEMATICS IN ENGINEERING, SCIENCE AND AEROSPACE, MESA -- www.journalmesa.com , Vol. 7, No. 2, pp. 339-347, 2016. @CSP -- Cambridge, UK; I&S -- Florida, USA, 2016.
• 138. Bhuvaneswari Sambandham and Aghalaya S Vatsala Generalized Monotone Method for Sequential Caputo Fractional Boundary Value Problems, Accepted for Publication in Journal of Advances in Applied Mathematics (JAAM 2016)

Refereed Research Publications in Proceedings:

• 1. "Reaction Diffusion Equations in Abstract Cones," Proceedings of the International Conference on Applied Nonlinear Analysis," 219-234, Academic Press (1979) (with V.Lakshmikantham and S.Leela).
• 2. "Existence and Asymptotic Behavior of Reaction Diffusion System via Coupled Quasi-solutions," Proceedings of the International Conference on Nonlinear Phenomena in Mathematical Sciences, Academic Press (1980) 619-628 (with G.S.Ladde and V.Lakshmikantham).
• 3. "Existence of Coupled Minimal and Maximal Periodic Quasi-Solutions for Systems of First Order Periodic Boundary Value Problem via Quasi-Solutions," Proceedings of the Fifth International Conference on Trends in Theory and Practice of Nonlinear Differential Equations', edited by V.Lakshmikantham, Marcel Dekker (1984) 541-546.
• 4. "Systems of First Order Partial Differential Equations and Monotone Iterative Technique," Proceedings of the sixth International Conference on 'Trends in Theory and Practice of Nonlinear Analysis, edited by V. Lakshmikantham, North Holland (1984) 249-255 (with G.S.Ladde).
• 5. "Monotone Iterative Technique for Singular Systems of Differential Equations," Proceedings of the International Conference on 'Nonlinear Analysis and Applications," Marcel Dekker (1987) 579-582.
• 6. "Existence of Solutions and Extremal Quasi-Solutions of the Nonlocal Problem," Proceedings of the Second International Colloquium on Differential Equations held at Plovdiv, Bulgaria, August 1992, World Scientific. (1992). edited by Drumi Bainov and Valery Covachev, 221-231.
• 7. "Modified Monotone Method for Solutions of Differential Equations," Proceedings of the International Conference on Theory and Applications of Differential Equations', (Edinburg, TX). Ordinary and Delay Differential Equations, (1992) Longman Scientific and Technical. 254-258.
• 8. "New Directions in the Method of Vector Lyapunov Functions via Perturbing Lyapunov Functions," Proceedings of the WCNA-92, pp. 1233-1238, 1996, Walter de Gruyter.
• 9. "Recent Advances in the Method of Quasilinerization," Proceedings of the Fourth Colloquium on Differential Equations, Plovdiv, Bulgaria, (1994), pp. 331-337,VSP International Science Publications.
• 10. "Stability Results of Nonlocal Reaction Diffusion Systems via Vector Lyapunov Functions," Proceedings of the Conference on Dynamic Systems and Applications, Vol. 1, (1994), pp 371-376.
• 11. "An Extension of the Method of Quasilinearization for Reaction Diffusion Equations," Proceedings of the Symposium on Comparison Methods and Stability Theory, Vol. 162, (1994), pp. 331-337, Marcel Dekker.
• 12. "Present Status on the Method of Generalized Quasilinearization", Proceedings of the Fifth Colloquium on Differential Equations, Plovdiv, Bulgaria, VSP International (1995), pp 345-352.
• 13. "Quadratic and Semiquadratic Convergence via Quasilinearization Method," (with D. Stutson), Proceedings of Neural, Parallel and Scientific Computation, 1 (1995) pp 441-444.
• 14. "Generalized Quasilinearization for Dynamic Systems on Time Scales and Superlinear Convergence," Proceedings of Dynamic Systems and Applications, 2, 333-340 (1996).
• 15. "Composite Boundedness and Stability Results via Perturbing Lyapunov Functions," Proceedings of Dynamic Systems and Applications, 2 529-534 (1996).
• 16. "Reflection and Dissipation of Acoustic Waves in an Isothermal Atmosphere," Proceedings of Dynamic Systems and Applications, 2, 45-52, (1996).
• 17. "Reaction Diffusion Equations with Fixed Moments of Impulse and Faster Convergence Methods," Proceedings of International Conference on Dynamical Systems and Differential Equations. VII, 267- 274, (1998).
• 18. "Impulsive Reaction-Diffusion System and Stability by Vector Lyapunov Functions", [Jointly with Xiaoquan Zhao] Proceedings of Dynamic Systems and Applications, pp 595-602, 3, (2001).
• 19. "The Extension of the Quasilinearization Method for Nonlocal Reaction Diffusion Equations", [Jointly with Liwen Wang], Proceedings of Dynamic Systems and Applications, 585-594, Vol. 3 (2001).
• 20. "On Existence and Quasilinearization Method for First Order Singular Initial Value Problems in Weighted Spaces," Jointly with J. Vasundhara Devi, Proceedings of the Third International Conference on Nonlinear Problems in Aviation and Aerospace, pp. 681-688, Vol. 2, 2001.
• 21. "Extended Method of Quasilinearization for Reaction Diffusion Systems",(with J. Vasundhara Devi) Proceedings of Neural, Parallel and Scientific Computation, 2, 273-276, (2002).
• 22. Practical Stability of Hybrid Impulsive Systems, Proceedings of the Fourth International Conference on Nonlinear Problems in Aviation and Aerospace, pp 519-5525, (2003).
• 23. Generalized Quasilinearization Method for Reaction Diffusion Equation with Numerical Applications, Jointly with J. Yang AIP Conference Proceedings Publishing Series 755, of the American Institute of Physics, pp 78-84, 2005.
• 24. Stability Results of Large-Scale Systems via Cone Valued Lyapunov Functions, jointly with V. Lakshmikantham, Proceedings of the 8th Conference on Dynamical Systems Theory Applications, Technical University of Lodz, Lodz, Poland,pp 2005.
• 25. Generalized Quasilinearization Method and Cubic Convergence for Integro-Differential Equations, (with Tanya G. Melton,) Proc. Neural, Parallel and Scientific Computation, V 3, 2006,PP 166- 170.
• 26. Generalized Quasilinearization Method and Fourth Order of Convergence for Integro-Differential Equations, Proceedings of the Union of Scientists - Ruse,Book 5, Mathematics, Informatics and Physics, Volume 6, 2006, pp. 11-19.(printed in 2007).
• 27. Generalized Quasilinearization Method and Higher Order of Convergence for Integro-Differential Equations (with Tanya G. Melton,) Proc. Proceedings of Dynamic Systems and Applications V5 , (2008) 317-321.
• 28. Fractional Differential and Integral Equations of Riemann-Liouville versus Caputo, to appear in Proceeding of the AMEE conference, AIP Conference Proceedings Publishing Series, (2008).
• 29. Improved Generalized Quasilinearization Method and Rapid Convergence for Nonlinear Volterra Integral Equations (with Tanya Melton) Proceeding of the AMEE conference,AIP Conference Proceedings Publishing Series, (2008).
• 30. Higher Order Convergence via Generalized Quasilinearization Method for Impulsive Differential Equations, (with Tanya Melton) Proceeding of the AMEE conference, AIP Conference Proceedings Publishing Series, 284- 291 (2009).
• 31. Fractional Differential Equations and Numerical Approxiamtions (With Z. Denon) Neural, Parallel and Scientific Computation, V 4, 2010, PP 119-123.
• 32. Third Order Convergence for the Periodic Boundary Value Problems for Impulsive Differential Equations (with Tanya Melton), Neural, Parallel and Scientific Computation, V 4, 2010, 273-278.
• 33. Generalized Monotone Method for Caputo Fractional Differential Equations with Periodic Boundary Conditions (with Diego Ramirez), Neural, Parallel and Scientific Computation, V 4, 2010, 332-337.
• 34. Cubic Convergence for Nonlinear Differential equations with Initial Time Difference (with Tanya Melton), Proceeding of the AMEE Conference, AIP Conference Proceedings Publishing Series, 107-114, (2010).
• 35. Third Order Convergence for Nonlinear Impulsive Differential Equations with a Nonlinear Three-Point Boundary Condition (with Tanya Melton), Citation: AIP Conf. Proc. 1404, 257 (2011); doi: 10.1063/1.3659928. View online: http://dx.doi.org/10.1063/1.3659928.
• 36. Third order convergence for forced duffing equations with three-point nonlinear boundary conditions (with Tanya G. Melton) Citation: AIP Conf. Proc. 1497, 239 (2012); doi: 10.1063/1.4766791. View online: http://dx.doi.org/10.1063/1.4766791.
• 37. A representative solution is obtained for the one dimensional Caputo Fractional Reaction Diffusion Equation, with Donna Stutson , Proceedings of Dynamic Systems and Applications 6 (2012) 1-2.
• 38. Third Order Convergence for Forced Duffingng Equations with Integral Boundary Conditions (with Tanya G. Melton) Citation: AIP Conference Proceedings 1570, 327 (2013); doi: 10.1063/1.4854773 View online: http://dx.doi.org/10.1063/1.4854773.
• 39. Amit Setia, Yucheng Liu and A. S. Vatsala, Solution of Linear fractional Fredholm integro-differential equation by using second kind Chebyshev Wavelet, 2014 11th International Conference on Information Technology: New Generations, pp 465-469, 978-1-4799-3187-3/14 2014 IEEE. DOI 10.1109/ITNG.2014.69.
• 40. Amit Setia, Yucheng Liu and A. S. Vatsala, The solution of the Bagley-Torvik equation by using second kind Chebyshev wavelet, 2014 11th International Conference on Information Technology: New Generations, pp 443 -467, 978-1-4799-3187-3/14 , 2014 IEEE, DOI 10.1109/ITNG.2014.68.

Research Monographs:

• 1. Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Publishing Co., 1985, (with G. S. Ladde and V. Lakshmikantham).
• 2. Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, 1998, (with V. Lakshmikantham).
• 3. Theory of Differential Equations in Cones, Cambridge Scientific Publishers, 2011, (with V. Lakshmikantham and S. Leela).