Aghalaya S. Vatsala
Professor

Contact:
Office: 406 Maxim Doucet
Phone: 337-482-5274
E-mail: asv5357@louisiana.edu
Home page: http://www.ucs.louisiana.edu/~asv5357

Degrees:
Ph.D. 1973 Indian Institute of Technology, Madras
M.S. 1968 Bangalore University, Bangalore, India
B.S. 1966 Bangalore University, Bangalore, India

Statement:
My main areas of research are ordinary and partial differential equations. My primary focuses are in the study of impulsive differential equations, reaction diffusion equations, differential equations with delay, integro-differential equations, singular systems and its applications. We develop numerical iterative procedures (yielding faster convergence) for the computation of solutions. Lyapunov stability theory, and stability in terms of two measures for large scale dynamical systems are my other major interests.

Selected research publications:

• Theory of Differential Equations in Cones (with V. Lakshmikantham and S. Leela), Cambridge University Press, in press.
• Fractional Integral Inequalities and Applications (With Zach Denton), Computers and Mathematics with Applications, 59 (2010), 1087--1094.
• Monotone Iterative Technique for Fractional Differential Equations with Periodic Boundary Conditions (with Diego Ramirez) Opuscula Mathematica, 29 (2009), 289--304.
• Inverse Problems for Coefficient Identification for Euler Bernoulli equation (with Tchavder Marinov) Computers and Mathematics with Applications, 56 (2008), 400--410.
• General Uniqueness and Monotone Iterative Technique for Fractional Differential Equations (with V. Lakshmikantham), Applied Mathematics Letter, (2008), 828--834.
• Basic Theory of Fractional Differential Equations (with V. Lakshmikantham), Nonlinear Analysis, 69 (2008), 3837--3343.
• Higher Order of Convergence via Generalized Quasilinearization Method for Parabolic Integro-Differential Equations (with Tanya Melton), Communication in Applied Analysis, 11 (2007), 403--418.
• Theory of Fractional Differential Inequalities and Applications (with V. Lakshmikantham), Communication in Applied Analysis, 11 (2007), 395--402.
• Generalized Monotone Iterative Method for Integro-Differential Equations with Periodic Boundary Conditions (with Ianna H. West), Mathematical Inequalities and Applications, 10 (2007), 151--163.
• Generalized Monotone Iterative Technique for Functional Differential Equations with Retardation and Anticipation, Nonlinear Dynamics and Systems Theory, 7 (2007), 431--438.
• Improved Generalized Method and Rapid Convergence for Reaction Diffusion Equations (with Tanya Melton), Applied Math and Computation, 203 (2008), 563--572.
• Stability in Terms of Two Measures of Hybrid Systems with Partially Visible Solutions (with V. Lakshmikantham and J. Vasundhara Devi), Nonlinear Analysis TMA special issue Hybrid Systems and Applications (1), 62 (2005), 1536--1543.
• Numerical Applications of Generalized Quasilinearization Method and Rapid Convergence (with Tanya Melton), Neural, Parallel and Scientific Computation, 12 (2004), 567--576.
• Monotone Iterative Technique for Semilinear Elliptic Systems (with J. Yang), Boundary Value Problems, 2 (2005), 93-106.
• Numerical Approach for the Solution of Reaction Diffusion Systems via Generalized Quasilinearization Method (with Jie Yang), Computers and Mathematics with Applications, 50 (2005), 587--598.
• Generalized Quasilinearization method and Higher Order of Convergence for First Order Initial Value Problems (with Tanya Melton), Dynamic Systems and Applications, 15 (2006), 375--394.
• Generalized Monotone Method for Second Order Boundary Value Problems (with Ianna H. West), Neural, Parallel and Scientific Computation, 13 (2005), 213--227.
• Basic Theory of Fuzzy Difference Equations (with V. Lakshmikantham), Journal of Difference Equations and Applications (Issue Dedicated to Professor Allan Peterson's 60th birthday), 8 (2002), 978--989.
• Generalized Monotone Technique for an Impulsive Differential Equation with Variable Moments of Impulse (with J. Vasundhara Devi), Nonlinear Studies, 9 (2002), 319--330.
• Extended Method of Quasilinearization for Systems of Nonlinear Differential Equations (with K. Vajravelu), Applicable Analysis, 74 (2000), 333--349.
• Existence of Fixed Points of Fuzzy Mappings Via Theory of Fuzzy Differential Equations (with V. Lakshmikantham), Journal of Computational and Applied Mathematics, 113 (2000), 195--200.
• Generalized Quasilinearization for Nonlinear Problems (with V.Lakshmikantham), Kluwer Academic Publishers, (1998).
• Monotone Iterative Techniques for Nonlinear Differential Equations (with G. S. Ladde and V. Lakshmikantham), Pitman Publishing Co., (1985).