Existence of solution involving Genocchi numbers for nonlocal anti-periodic boundary value problem of arbitrary fractional order

Abstract

In this article, we investigate the existence of solutions for boundary value problem of fractional differential equations with anti-periodic and fractional integral boundary conditions. The obtained solution contains the so-called Genocchi coefficients. The existence results are obtained by applying Banach’s contraction mapping principle, Schauder’s fixed point theorem, Leray-Schauder degree theory, and Krasnoselskii’s fixed point. An example is introduced to explain the applicability of these theorems.