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Ulam–Hyers Stability of Fuzzy Fractional Non-instantaneous Impulsive Switched Differential Equations Under Generalized Hukuhara Differentiability

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Abstract

This paper is devoted to studying a class of fuzzy fractional switched implicit differential equations (FFSIDEs) with non-instantaneous impulses that there are few papers considering this issue. Considering switching law and the memory property of fractional calculus, we first present a formula of solution for FFSIDEs with non-instantaneous impulses. Subsequently, based on a sequence of Picard functions, we explore the existence of solutions for the addressed equations by successive approximation. Furthermore, Ulam–Hyers (U–H) stability for this considered equations is derived. The main results are obtained using fuzzy-valued fractional calculus and nonlinear analysis. Finally, two numerical examples illustrating the theoretical result are given.

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Acknowledgements

The author thanks reviewers for their valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Jizhao Huang & Danfeng Luo

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  1. Jizhao Huang
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  2. Danfeng Luo
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Correspondence to Danfeng Luo.

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Huang, J., Luo, D. Ulam–Hyers Stability of Fuzzy Fractional Non-instantaneous Impulsive Switched Differential Equations Under Generalized Hukuhara Differentiability. Int. J. Fuzzy Syst. 26, 1481–1492 (2024). https://doi.org/10.1007/s40815-024-01681-8

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  • DOI: https://doi.org/10.1007/s40815-024-01681-8

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