Fixed Point Results for the Fractional Nonlinear Problem with Integral Boundary Condition

In this article, we study an integral boundary condition problem. In fact, we consider a new nonlinear fractional integro-differential equation with arbitrary order and integral boundary condition. We show that there is a unique solution for this type of equation according to Babenko’s strategy and the multivariate Mittag–Leffler function. All results, including the existence problem, are proved using Banach’s contractive principle and Leray–Schauder’s fixed point theorem. Several examples are also presented to demonstrate applications of the proven theorems.