Nonlinear Implicit Caputo-Hadamard Fractional Differential Equation with Fractional Boundary Conditions

Abstract

In this paper, we establish the existence and uniqueness of solutions for a class of problem for nonlinear implicit fractional differential equations of Caputo-Hadamard type with fractional boundary conditions. The results are obtained by using Banach fixed point theorem and Schauder’s fixed point theorem. An example is included to show the applicability of our results.

Key words and phrases. Boundary value problem, CaputoHadamard fractional derivative, Implicit fractional differential equations, Fixed point theorems, Existence and uniqueness.

2020 Mathematics Subject Classification. 26A33, 34A09, 34B10