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Stability of Nonlinear Implicit Differential Equations with Caputo–Katugampola Fractional Derivative

Author

Listed:
  • Qun Dai

    (School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, China)

  • Yunying Zhang

    (School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, China)

Abstract

The purpose of this paper is to study nonlinear implicit differential equations with the Caputo–Katugampola fractional derivative. By using Gronwall inequality and Banach fixed-point theorem, the existence of the solution of the implicit equation is proved, and the relevant conclusions about the stability of Ulam–Hyers are obtained. Finally, the correctness of the conclusions is verified by an example.

Suggested Citation

  • Qun Dai & Yunying Zhang, 2023. "Stability of Nonlinear Implicit Differential Equations with Caputo–Katugampola Fractional Derivative," Mathematics, MDPI, vol. 11(14), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3082-:d:1192641
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    References listed on IDEAS

    as
    1. Manzoor Ahmad & Jiqiang Jiang & Akbar Zada & Syed Omar Shah & Jiafa Xu, 2020. "Analysis of Coupled System of Implicit Fractional Differential Equations Involving Katugampola–Caputo Fractional Derivative," Complexity, Hindawi, vol. 2020, pages 1-11, April.
    2. Rabha W. Ibrahim, 2012. "Ulam-Hyers Stability for Cauchy Fractional Differential Equation in the Unit Disk," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, July.
    3. McSylvester Ejighikeme Omaba & Hamdan Al Sulaimani, 2022. "On Caputo–Katugampola Fractional Stochastic Differential Equation," Mathematics, MDPI, vol. 10(12), pages 1-12, June.
    4. Muhammad Nadeem & Zitian Li & Yahya Alsayyad & Ibrahim Mahariq, 2022. "Analytical Approach for the Approximate Solution of Harry Dym Equation with Caputo Fractional Derivative," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-7, October.
    5. Leila Sajedi & Nasrin Eghbali & Hassen Aydi & Xiaolong Qin, 2021. "Impulsive Coupled System of Fractional Differential Equations with Caputo–Katugampola Fuzzy Fractional Derivative," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, October.
    6. Rabha W. Ibrahim, 2012. "Ulam Stability for Fractional Differential Equation in Complex Domain," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, January.
    7. Minh Duc Tran & Vu Ho & Hoa Ngo Van, 2020. "On the Stability of Fractional Differential Equations Involving Generalized Caputo Fractional Derivative," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-14, February.
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