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Generalized Grönwall Inequality and Ulam–Hyers Stability in ℒ p Space for Fractional Stochastic Delay Integro-Differential Equations

Author

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  • Abdelhamid Mohammed Djaouti

    (Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Al Hofuf 31982, Saudi Arabia)

  • Muhammad Imran Liaqat

    (Department of Mathematics, National College of Business Administration & Economics, Lahore 54000, Pakistan)

Abstract

In this work, we derive novel theoretical results concerning well-posedness and Ulam–Hyers stability. Specifically, we investigate the well-posedness of Caputo–Katugampola fractional stochastic delay integro-differential equations. Additionally, we develop a generalized Grönwall inequality and apply it to prove Ulam–Hyers stability in L p space. Our findings generalize existing results for fractional derivatives and space, as we formulate them in the Caputo–Katugampola fractional derivative and L p space. To support our theoretical results, we present an illustrative example.

Suggested Citation

  • Abdelhamid Mohammed Djaouti & Muhammad Imran Liaqat, 2025. "Generalized Grönwall Inequality and Ulam–Hyers Stability in ℒ p Space for Fractional Stochastic Delay Integro-Differential Equations," Mathematics, MDPI, vol. 13(8), pages 1-23, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1252-:d:1632219
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    References listed on IDEAS

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    1. Ahmed, Hamdy M. & El-Borai, Mahmoud M., 2018. "Hilfer fractional stochastic integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 182-189.
    2. 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.
    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. Anwarud Din & Yongjin Li & Faiz Muhammad Khan & Zia Ullah Khan & Peijiang Liu, 2022. "On Analysis Of Fractional Order Mathematical Model Of Hepatitis B Using Atangana–Baleanu Caputo (Abc) Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-18, February.
    5. 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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