On differential equations involving the ψ$$ \psi $$‐shifted fractional operators

Abstract

This paper is in concern with the study of differential problems involving the ‐shifted fractional derivatives, where is a scaling function. Such operators can be thought of as a generalization of several fractional derivatives such as the classical Riemann–Liouville and Caputo operators, the Hadamard operators, the generalized fractional operators, and the Erdélyi–Kober operators, among others. Two types of boundary conditions are considered: the Cauchy problems and the integral boundary conditions.