Fractional Differential Equations and Inclusions with Nonlocal Generalized Riemann-Liouville Integral Boundary Conditions

Abstract

In this paper, we study a new kind of nonlocal boundary value problems of nonlinear fractional differential equations and inclusions supplemented with nonlocal and generalized Riemann-Liouville fractional integral boundary conditions. In case of single valued maps (equations), we make use of contraction mapping principle, fixed point theorem due to Sadovski, Krasnoselskii-Schaefer fixed point theorem due to Burton and Kirk, and fixed point theorem due to O’Regan to obtain the desired existence results. On the other hand, the existence results for inclusion case are based on Krasnoselskii’s fixed point theorem for multivalued maps and nonlinear alternative for contractive maps. Examples illustrating the main results are also constructed.