Method of Upper Lower Solutions for Fractional Integro Diffusion Equation

Abstract

The purpose of this paper is to develop method  of upper lower solutions for nonlinear fractional integro diffusion equation and prove existence and uniqueness of solution.We introduce the notion of upper lower solutions and choose upper  solution  as an initial iteration and  construct monotone sequence, which converges monotonically from above to maximal solution. We choose lower solution as an initial iteration and construct monotone sequence, which converges monotonically from below to  minimal solution.