Existence results for nonlinear fractional boundary value problem involving generalized proportional derivative

Abstract

Abstract We introduce nonlinear fractional BVPs including a generalized proportional derivatives with nonlocal multipoint and substrip boundary conditions. The nonlinearities are defined on the Orlicz space and depend on the unknown function and its generalized derivative. Existence results for a nonlinear boundary value problem involving a proportional fractional derivative by utilizing some fixed point theorems are presented. The obtained results are new and are well illustrated with an example.

Keywords

• Generalized proportional derivative
• Fractional boundary value problem
• Orlicz spaces