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Stability Analysis for Differential Equations of the General Conformable Type

Author

Listed:
  • Abdellatif Ben Makhlouf
  • El-Sayed El-Hady
  • Salah Boulaaras
  • Mohamed Ali Hammami

Abstract

Fractional calculus is nowadays an efficient tool in modelling many interesting nonlinear phenomena. This study investigates, in a novel way, the Ulam–Hyers (HU) and Ulam–Hyers–Rassias (HUR) stability of differential equations with general conformable derivative (GCD). In our analysis, we employ some version of Banach fixed‐point theory (FPT). In this way, we generalize several earlier interesting results. Two examples are given at the end to illustrate our results.

Suggested Citation

  • Abdellatif Ben Makhlouf & El-Sayed El-Hady & Salah Boulaaras & Mohamed Ali Hammami, 2022. "Stability Analysis for Differential Equations of the General Conformable Type," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:7283252
    DOI: 10.1155/2022/7283252
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Sadek Gala & Maria Alessandra Ragusa, 2020. "A Regularity Criterion in Weak Spaces to Boussinesq Equations," Mathematics, MDPI, vol. 8(6), pages 1-11, June.
    2. SunAe Pak & KumSong Jong & KyuNam O & HuiChol Choi, 2020. "Existence Results for a Class of - Laplacian Fractional Differential Equations with Integral Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-11, May.
    3. HuiChol Choi & YongSim Sin & KumSong Jong, 2020. "Existence Results for Nonlinear Multiorder Fractional Differential Equations with Integral and Antiperiodic Boundary Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    4. Ferrag Azouz & Djalal Boucenna & Abdellatif Ben Makhlouf & Lassaad Mchiri & Abbes Benchaabane & Carlos Aguilar-Ibanez, 2021. "Controllability of Differential Systems with the General Conformable Derivative," Complexity, Hindawi, vol. 2021, pages 1-11, October.
    5. HuiChol Choi & YongSim Sin & KumSong Jong, 2020. "Existence Results for Nonlinear Multiorder Fractional Differential Equations with Integral and Antiperiodic Boundary Conditions," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-9, April.
    6. Kui Liu & Michal Fečkan & JinRong Wang, 2020. "A Fixed-Point Approach to the Hyers–Ulam Stability of Caputo–Fabrizio Fractional Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    7. SunAe Pak & KumSong Jong & KyuNam O & HuiChol Choi, 2020. "Existence Results for a Class of p -Laplacian Fractional Differential Equations with Integral Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
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