Existence Uniqueness Continuation and Stability of Variable Order Caputo Type Fractional Differential Equations with Delay

Abstract

In this paper, we discuss about the existence, uniqueness and continuation of Caputo type Variable Order Fractional Delay Differential Equation (VOFDDE)

{█(〖(_C^)D〗_(0,t)^s(t)  y(t)=f(t,y(t),y(t-τ)),0<s(t)<1@y(t)=y_0   at t=0,y∈R,t∈(0,∞))┤

We extend the continuation theorem for the variable order fractional delay differential equation and then we present different types of Ulam–Hyers stability results for the Caputo type VOFDDE