New Existence of Solutions for Fractional Integro-Differential Equations with Nonseparated Boundary Conditions

Abstract

Results reported in this article prove the existence and uniqueness of solutions for a class of nonlinear fractional integro-differential equations supplemented by nonseparated boundary value conditions. We consider a new norm to establish the existence of solution via Krasnoselskii fixed point theorem; however, the uniqueness results are obtained by applying the contraction mapping principle. Some examples are provided to illustrate the results.

The Existence and Uniqueness of Solution to Sequential Fractional Differential Equation with Affine Periodic Boundary Value Conditions

“…More and more scholars pay attention to this subject and achieve many excellent results. For instance, see [5][6][7][8][9][10][11] and the references therein. There are many types of boundary value problem, including the integral boundary value problem, multipoint boundary value problem, and periodic boundary value problem.…”