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      • Record: found
      • Abstract: found
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      Is Open Access

      Stability of some generalized fractional differential equations in the sense of Ulam–Hyers–Rassias

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          Abstract

          In this paper, we investigate the existence and uniqueness of fractional differential equations (FDEs) by using the fixed-point theory (FPT). We discuss also the Ulam–Hyers–Rassias (UHR) stability of some generalized FDEs according to some classical mathematical techniques and the FPT. Finally, two illustrative examples are presented to show the validity of our results.

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          Most cited references32

          • Record: found
          • Abstract: not found
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          On the stability of the linear mapping in Banach spaces

          Themistocles Rassias (1978)
          Article 0 comments Cited 229 times – based on 0 reviews     Review now
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            On the Stability of the Linear Functional Equation.

            D H Hyers (1941)
            Article 0 comments Cited 129 times – based on 0 reviews     Review now
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              On stability of additive mappings

              Zbigniew Gajda (1991)
              In this paper we answer a question of Th. M. Rassias concerning an extension of validity of his result proved in [3].
              Article 0 comments Cited 120 times – based on 0 reviews     Review now
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                Author and article information

                Contributors
                Abdellatif Ben Makhlouf: abmakhlouf@ju.edu.sa
                Journal
                Journal ID (nlm-ta): Bound Value Probl
                Journal ID (iso-abbrev): Bound Value Probl
                Title: Boundary Value Problems
                Publisher: Springer International Publishing (Cham )
                ISSN (Print): 1687-2762
                ISSN (Electronic): 1687-2770
                Publication date (Electronic): 26 January 2023
                Publication date PMC-release: 26 January 2023
                Publication date (Print): 2023
                Volume: 2023
                Issue: 1
                Electronic Location Identifier: 8
                Affiliations
                [1 ]GRID grid.440748.b, ISNI 0000 0004 1756 6705, Mathematics Department, College of Science, , Jouf University, ; P.O. Box: 2014, Sakaka, Saudi Arabia
                [2 ]GRID grid.412602.3, ISNI 0000 0000 9421 8094, Department of Mathematics, College of Sciences and Arts, ArRass, , Qassim University, ; Buraydah, Saudi Arabia
                [3 ]GRID grid.412124.0, ISNI 0000 0001 2323 5644, Department of Mathematics, Faculty of Sciences of Sfax, , University of Sfax, ; Route Soukra, BP 1171, 3000 Sfax, Tunisia
                [4 ]GRID grid.8390.2, ISNI 0000 0001 2180 5818, ENSIIE, , University of Evry-Val-d’Essonne, ; 1 square de la Résistance, 91025 Évry-Courcouronnes Cedex, France
                Article
                Publisher ID: 1695
                DOI: 10.1186/s13661-023-01695-5
                PMC ID: 9879255
                SO-VID: 717e6b19-2c48-4c08-a4a7-555b656b63a3
                Copyright © © The Author(s) 2023
                License:

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

                History
                Date received : 27 September 2022
                Date accepted : 17 January 2023
                Categories
                Subject: Research
                Custom metadata
                issue-copyright-statement © The Author(s) 2023

                Keywords: 47h10,47j05,hyers–ulam–rassias stability,generalized fractional differential equation,fixed-point theory
                Data availability:
                Keywords: 47h10, 47j05, hyers–ulam–rassias stability, generalized fractional differential equation, fixed-point theory

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