Aghalaya S. Vatsala

Pennzoil Endowed Professor
Applied Mathematics

406 Maxim Doucet Hall
337-482-5274
vatsala@louisiana.edu

Aghalaya S. Vatsala's webpage

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

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:

• Zachary Denton and Vatsala, A. S.,
  Existence in the Large for Caputo Fractional Multi-Order Systems with Initial Conditions,
  Foundations, 3 (2023), 260-274.
  

  ---

• Vatsala, A. S. and Pageni, Govinda,
  Caputo Sequential Fractional Differential Equations with Applications,
  in Synergies in Analysis, Discrete Mathematics, Soft Computing and Modelling, Forum for Interdisciplinary Mathematics Series, Springer, (2023), 83-102.
  

  ---

• Antony Vijesh, V. and Vatsala, A. S.
  An accelerated technique for the coupled system of reaction-diffusion-transport equations arising from catalytic converters
  J. Math. Anal. Appl., 515, (2022) 2, Paper No. 126365, 39.
  

  ---

• Vatsala, A. S., Pageni, Govinda and Vijesh, V. Anthony,
  Analysis of Sequential Caputo Fractional Differential Equations versus Non-Sequential Caputo Fractional Differential Equations with Applications,
  Foundations 2, (2022), 1129-1142.
  

  ---

• Govinda Pageni and Aghalaya S Vatsala,
  Study of Two System of Caputo Fractional Differential Equations with Initial Conditions via Laplace Transform Method,
  Neural Parallel and Scientific Computations, 29, (2021), No. 2, 69-83.
  

  ---

• Govinda Pageni and Aghalaya S Vatsala,
  Study of Three Systems of Non-Linear Caputo Fractional Differential Equations with Initial Conditions and Applications
  Neural Parallel and Scientific Computations, 29, (2021), No. 4, 211-229.
  

  ---

• Bai, Y. and Vatsala, A. S.,
  Numerical results for sequential sub hyperbolic equation in one dimensional space,
  Mathematics in Engineering, Science and Aerospace 11 (2020) no. 3, 595-611.
  

  ---

• A.S. Vatsala and Bhuvaneswari Sambandham,
  Sequential Caputo versus Nonsequential Caputo Fractional Initial and Boundary Value Problems,
  International Journal of Difference Equations 15 (2020) no. 2, 529–544.
  

  ---

• Subhash Subedi and Vatsala, A.S.
  Quenching Problem for Two Dimensional Caputo Time-Fractional Reaction-Diffusion Equation
  Dynamic Systems and Applications 29 (2020) no. 1, 26-52.
  

  ---

• Bai, Y. and Vatsala, A. S.,
  Generalized monotone method for nonlinear Caputo fractional impulsive differential equations,
  Nonlinear Dyn. Syst. Theory, 20, (2020) 1, 3-20.
  

  ---