Existence Results for Nonlinear Multiorder Fractional Differential Equations with Integral and Antiperiodic Boundary Conditions

Abstract

In this paper, we study the solvability of a class of nonlinear multiorder Caputo fractional differential equations with integral and antiperiodic boundary conditions. By using some fixed point theorems including the Banach contraction mapping principle and Schaefer’s fixed point theorem, we obtain new existence and uniqueness results for our given problem. Also, we give some examples to illustrate our main results.

Existence and uniqueness of solutions for multi-order fractional differential equations with integral boundary conditions

“…Remark 2. This paper is motivated greatly by [24]. Compared with [24], the existence results in this paper are established under new and simpler conditions, which indicates that our works are not a trivial generalization of [24].…”

“…In 2020, Choi et al [24] investigated the existence and uniqueness of solutions to the BVP of nonlinear multi-order fractional differential equation…”