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.
@article{arxiv.1805.05546,
title = {On the stability of a hyperbolic fractional partial differential equation},
author = {J. Vanterler da C. Sousa and E. Capelas de OLiveira},
journal= {arXiv preprint arXiv:1805.05546},
year = {2018}
}