Existence Results for a Differential Equation Involving the Right Caputo Fractional Derivative and Mixed Nonlinearities with Nonlocal Closed Boundary Conditions

Abstract

In this study, we present a new notion of nonlocal closed boundary conditions. Equipped with these conditions, we discuss the existence of solutions for a mixed nonlinear differential equation involving a right Caputo fractional derivative operator, and left and right Riemann–Liouville fractional integral operators of different orders. We apply a decent and fruitful approach of fixed point theory to establish the desired results. Examples are given for illustration of the main results. The paper concludes with some interesting observations.