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Aghalaya S. Vatsala

Aghalaya S. Vatsala
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:

  • Generalized monotone method for fractional reaction diffusion equations (with Stutson, Donna), Commun. Appl. Anal., 16 (2012), 165--173.
  • Generalized quasilinearization method for RL fractional differential equations (with Denton, Z.), Nonlinear Stud., 19 (2012), 637--652.
  • Generalized monotone method for Caputo fractional differential equation with applications to population models (with Pham, Th. T. and Ramírez, J. D.), Neural Parallel Sci. Comput., 20 (2012), 119--132.
  • Generalized monotone iterative technique for Caputo fractional differential equation with periodic boundary condition via initial value problem (with Ramírez, J. D.), Int. J. Differ. Equ., (2012), Art. ID 842813, 17 pp.
  • Generalized monotone method for Caputo fractional differential systems via coupled lower and upper solutions (with Stutson, Donna), Dynam. Systems Appl., 20 (2011), 495--503.
  • Quasilinearization method via lower and upper solutions for Riemann-Liouville fractional differential equations (with Denton, Z. and Ng, P. W.), Nonlinear Dyn. Syst. Theory, 11 (2011), 239--251.
  • Monotone method for nonlinear Caputo fractional boundary value problems (with Ramírez, J. D.), Dynam. Systems Appl., 20 (2011), 73--88.
  • Monotone iterative technique for finite systems of nonlinear Riemann-Liouville fractional differential equations (with Denton, Z.), Opuscula Math., 31 (2011), 327--339.
  • Generalized monotone iterative technique for impulsive differential systems (with West, Ianna H.), Commun. Appl. Anal., 14 (2010), 301--310.
  • Theory of Differential Equations in Cones (with V. Lakshmikantham and S. Leela), Cambridge Scientific Publishers, (2011).