Abstract:
The present work is basically devoted to study the existence and uniqueness of solutions
for certain classes of nonlinear fractional differential equations with initial conditions via
the ψ−Caputo fractional derivative with order α ∈ (0;1). To achieve these goals, we first
transform our main problems into an equivalent fractional integral equation. After that, based
on some fixed point theorems namely, Banach’s fixed point theorem combined with the ψ-
fractional Bielecki norm, Schauder’s fixed point theorem, and Krasnoselskii’s fixed point
theorem, the existence, and uniqueness of solutions to the proposed problems are discussed
theoretically. Furthermore, examples are presented to illustrate our theoretical findings.
