Caputo Type Fractional Differential Equations with Nonlocal Riemann-Liouville and Erdelyi-Kober Type Integral Boundary Conditions

Abstract

In this paper, we study nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with different combinations of Riemann-Liouville and Erd\'elyi-Kober type fractional integral boundary conditions. By applying a variety of tools of fixed point theory, the desired existence and uniqueness results are obtained. Examples illustrating the main results are also constructed.