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Applications of the Mittag–Leffler function in solvability and stability of a class of fractional Langevin equations with two fractional orders

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Abstract

This study focuses on the solvability and Hyers–Ulam stability of a particular class of fractional Langevin equations with two fractional orders. Utilizing the Mittag–Leffler functions, we present a representation of the general solution for the problem. Our approach offers significant technical advantages compared to existing literature. Furthermore, we furnish illustrative examples, employing specific parameters, to showcase the existence of a unique solution and its Hyers–Ulam stability even under less restrictive conditions.

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Funding

The research of J.J. Nieto was supported by a research grant of the Agencia Estatal de Investigacion, Spain, Grant PID2020-113275GB-I00 funded by MCIN/AEI/ 10.13039/501100011033 and by “ERDF A way of making Europe”, by the “European Union”.

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran

    Hamid Baghani

  2. CITMAga, Department of Statistics, Mathematical Analysis and Optimization, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto

Authors
  1. Hamid Baghani
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  2. Juan J. Nieto
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Correspondence to Hamid Baghani.

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Communicated by S. Ponnusamy.

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Baghani, H., Nieto, J.J. Applications of the Mittag–Leffler function in solvability and stability of a class of fractional Langevin equations with two fractional orders. J Anal 32, 915–929 (2024). https://doi.org/10.1007/s41478-023-00669-1

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  • DOI: https://doi.org/10.1007/s41478-023-00669-1

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