Existence of Solutions for Integrodifferential Equations of Fractional Order with Antiperiodic Boundary Conditions

Recently, the subject of fractional differential equations has emerged as an important area of investigation. Fractional differential equations arise in many engineering and scientific disciplines as the fractional derivatives describe numerous events and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, and so forth. For some recent development on the subject, see 1–15 and the references therein. Integrodifferential equations arise inmany engineering and scientific disciplines, often as approximation to partial differential equations, which represent much of the continuum phenomena. Many forms of these equations are possible. For details, see 16–20 and the references therein. Antiperiodic boundary value problems have recently received considerable attention as antiperiodic boundary conditions appear in numerous situations, for instance, see 21–25 . In this paper, we prove some existence and uniqueness results for the following antiperiodic fractional boundary value problem: