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

https://doi.org/10.46719/dsa20202913

ABSTRACT.
In this paper, we study the quenching problem for Caputo time-fractional reaction-
diffusion equation with a nonlinear reaction term in two dimensional rectangular domain. In this work, we prove local existence and the quenching of the solution of Caputo fractional ordinary differential equation and Caputo fractional reaction-diffusion equation with a nonlinear reaction term in finite time. We establish the condition for quenching for the solution of fractional ordinary differential equation and fractional reaction-diffusion equation. We also provide the upper bound for the quenching time of the solution of fractional ordinary and reaction-diffusion equation. The study of quenching behavior of the solution of fractional differential equation relies on the quenching behavior of the solution of integer order reaction-diffusion equation and method of upper and lower solution.

AMS (MOS) Subject Classification. 39A10.