Stability Results for the Darboux Problem of Conformable Partial Differential Equations-Reference-Cited by-同舟云学术

Stability Results for the Darboux Problem of Conformable Partial Differential Equations

Published:2023-06-28 Issue:7 Volume:12 Page:640
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Ghania Rebiai¹,Mchiri Lassaad²,Rhaima Mohamed³^ORCID,Hannabou Mohamed⁴,Ben Makhlouf Abdellatif⁵^ORCID

Affiliation:

1. Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 2400, Algeria

2. ENSIIE, University of Evry-Val-d’Essonne, 1 Square de la Résistance, 91025 Évry-Courcouronnes, France

3. Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

4. Department of Mathematics, Faculty of Sciences and Technics, Sultan Moulay Slimane University, BP 523, Beni Mellal 23000, Morocco

5. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Route Soukra, BP 1171, Sfax 3000, Tunisia

Abstract

In this paper, we investigate the Darboux problem of conformable partial differential equations (DPCDEs) using fixed point theory. We focus on the existence and Ulam–Hyers–Rassias stability (UHRS) of the solutions to the problem, which requires finding solutions to nonlinear partial differential equations that satisfy certain boundary conditions. Using fixed point theory, we establish the existence and uniqueness of solutions to the DPCDEs. We then explore the UHRS of the solutions, which measures the sensitivity of the solutions to small perturbations in the equations. We provide three illustrative examples to demonstrate the effectiveness of our approach.

Funder

King Saud University, Riyadh, Saudi Arabia

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/7/640/pdf

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