Fractional boundary value problem with $$\varvec{\psi }$$
                  ψ
                -Caputo fractional derivative

Mohammed S Abdo; Satish K Panchal; Abdulkafi M Saeed

doi:10.1007/s12044-019-0514-8

Fractional boundary value problem with $$\varvec{\psi }$$ ψ -Caputo fractional derivative

Mohammed S Abdo, Satish K Panchal, Abdulkafi M Saeed

Source

Proceedings - Mathematical Sciences > 2019 > 129 > 5 > 1-14

Abstract

This paper is concerned with a boundary value problem for a nonlinear fractional differential equation involving a general form of Caputo fractional derivative operator with respect to new function $$\psi $$ ψ . The existence and uniqueness results of solutions are obtained. Our analysis relies on a variety of tools of fractional calculus together with fixed point theorems of Banach and Schaefer. The investigation of the results will be illustrated by providing a suitable example.