On the stability of a hyperbolic fractional partial differential equation

2018/05/15 by J. Vanterler da C. Sousa, Sousa, J. Vanterler da C., E. Capelas de Oliveira +1
Mathematics · #26A33 #35B35 #35LXX #35R11 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Equations Stability Results #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1805.05546

openalex publication_date 2018/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, by means of the Gronwall inequality, the ψ-Riemann-Liouville fractional partial integral and the ψ-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.

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