Boundary Value Problems for Nonlinear Fractional Differential Equations and Inclusions with Nonlocal and Fractional Integral Boundary Conditions

Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. These characteristics of the fractional derivatives make the fractional-order models more realistic and practical than the classical integer-order models. In recent years, boundary value problems for nonlinear fractional differential equations have been addressed by several researchers. As a matter of fact, fractional differential equations arise in many engineering and scientific disciplines such as physics, chemistry, biology, economics, control theory, signal and image processing, biophysics, blood flow phenomena, aerodynamics, fitting of experimental data, etc. [26, 32–34]. For some recent development on the topic, see [1–13,15,27,29,35,36] and the references therein.