A Study of Nonlinear Fractional-Order Boundary Value Problem with Nonlocal Erdelyi-Kober and Generalized Riemann-Liouville Type Integral Boundary Conditions

Abstract

We investigate a new kind of nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with integral boundary conditions involving Erdelyi-Kober and generalized Riemann-Liouville fractional integrals. Existence and uniqueness results for the given problem are obtained by means of standard fixed point theorems. Examples illustrating the main results are also discussed.

Keywords

• Caputo fractional derivative
• Erdelyi-Kober
• generalized Riemann-Liouville fractional integral
• fractional integral
• fixed point