Abstract

not-yet-known not-yet-known not-yet-known unknown The regularized ψ-Hilfer derivative within the sense of Caputo is an improved version of the ψ-Hilfer fractional derivative, primarily because it addresses the issue where the initial conditions of problems involving the ψ-Hilfer fractional derivative lack clear physical significance unless p=1. This article’s main contribution is the use of the ψ-Laplace transform, which is the first provide an explicit expression for mild solutions to the fractional diffusion equations with the regularized ψ-Hilfer derivative. Additionally, we investigate the existence and attractivity of mild solutions for fractional diffusion equations involving the regularized ψ-Hilfer fractional derivatives. Finally, we provide two examples to illustrate our main resuits.