A quenching problem of Kawarada's type for one dimensional Caputo fractional reaction diffusion equation

Abstract

We study the quenching problems of Kawarada's type for Caputo-fractional reaction diffusion equation in one dimensional space. We have developed maximum principle and comparison result relative to the linear Caputo fractional reaction diffusion equation in one dimension. In this work, we prove that the Caputo time derivative fractional reaction diffusion equation quenches by two different methods. The methods used here are by comparing the Picard's iterates of the Caputo fractional reaction diffusion equation with that of the Picard's iterates of the Kawarda's ordinary reaction reaction diffusion equation. The second method is by upper and lower solution method.