Some results on a nonlinear fractional equation with nonlocal boundary condition

Abstract

The aim of this paper is to derive sufficient conditions for the existence, uniqueness, and Hyers–Ulam stability of solutions to a new nonlinear fractional integro‐differential equation with functional boundary conditions, using several fixed‐point theorems, the multivariate Mittag‐Leffler function and Babenko's approach. A few examples are also presented to illustrate the applications of our results based on approximate values of a couple of Mittag‐Leffler functions calculated by Python codes. Furthermore, the approaches used have a wide range of applications to various fractional differential equations with initial or boundary conditions or integral equations in complete spaces.