Boundary and initial value problem for nonlinier of Caputo-Katugampola type fractional differential equation

Abstract

T he aim of memory is to study the existence and uniqueness of solution to boundary value prob￾lem of nonlinear fractional differential equation with Caputo-Katugampola derivative in bounded domain. The derived results are based on fixed point theorems (Banach’s, Schauder’s, Schaufer’s). Next, we establish the existence of solution to a certain coupled system of Caputo-Katugampola fractional dif￾ferential equation. We conclude the results obtained by illustrative examples.