Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions

Abstract

This paper studies the existence of solutions for nonlinear fractional differential equations and inclusions of order q ∈ ( 3 , 4 ] with anti-periodic boundary conditions. In the case of inclusion problem, the existence results are established for convex as well as nonconvex multivalued maps. Our results are based on some fixed point theorems, Leray–Schauder degree theory, and nonlinear alternative of Leray–Schauder type. Some illustrative examples are discussed.