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Existence and Stability Results for Nonlinear Implicit Random Fractional Integro-Differential Equations

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Abstract

In this typescript, we present nonlinear implicit random fractional integro-differential equation in mean square sense and its corresponding coupled system. For the existence, uniqueness and at least one solution of the said nonlinear equation, we use Banach contraction and Schauder fixed point theorems, respectively. Uniqueness and at least one solution of corresponding coupled form of the proposed nonlinear system will be prove through Banach contraction theorem and Arzel\(\grave{\textrm{a}}\)–Ascoli theorem, respectively. Under some hypothesis, we scrutinize Hyers–Ulam stability of the mentioned nonlinear equation and its corresponding coupled nonlinear system. For the support of our main results, we present examples.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, KSA, for funding this work through Research Group under grant number (R.G.P-1/3/43).

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan

    Sumbel Shahid, Shahid Saifullah & Akbar Zada

  2. Department of Physical and Numerical Sciences, Qurtuba University of Science and Information Technology, Peshawar, Pakistan

    Usman Riaz

  3. Faculty of Science and Arts, Mohail Asser, King Khalid University, Abha, Saudi Arabia

    Sana Ben Moussa

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  1. Sumbel Shahid
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  2. Shahid Saifullah
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The authors have contributed equally to this manuscript. They read and approved the final manuscript.

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Shahid, S., Saifullah, S., Riaz, U. et al. Existence and Stability Results for Nonlinear Implicit Random Fractional Integro-Differential Equations. Qual. Theory Dyn. Syst. 22, 81 (2023). https://doi.org/10.1007/s12346-023-00772-5

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