On the stability of a hyperbolic fractional partial differential equation

TL;DR

This paper investigates the stability of solutions to a hyperbolic fractional partial differential equation using advanced fractional calculus tools, providing new insights into their Ulam-Hyers stability in Banach spaces.

Contribution

It introduces new fractional derivatives and integrals, and applies them to analyze the stability of hyperbolic fractional PDEs, extending existing stability results.

Findings

Established Ulam-Hyers stability conditions for the fractional PDE

Derived new fractional integral and derivative formulas

Revealed particular cases of the stability analysis

Abstract

In this paper, by means of the Gronwall inequality, the {\psi}-Riemann-Liouville fractional partial integral and the {\psi}-Hilfer fractional partial derivative are introduced and some of its particular cases are recovered. Using these results, we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the solutions of a fractional partial differential equation of hyperbolic type in a Banach space (B, |.|), real or complex.