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Some New Properties of the Mittag-Leffler Functions and Their Applications to Solvability and Stability of a Class of Fractional Langevin Differential Equations

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Abstract

The paper examines the solvability and stability of a particular set of fractional Langevin equations under anti-periodic boundary conditions. Utilizing the Krasnoselskii fixed point theorem, the Banach contraction mapping theorem, and properties of the Mittag-Leffler function, we establish less stringent criteria for the existence and uniqueness of solutions compared to previous findings in the literature. Furthermore, we present illustrative examples with specific parameters that highlight the reduced conditions necessary for ensuring the existence of a unique solution.

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Acknowledgements

The authors would like to express their sincere gratitude to the editor and three anonymous referees for their useful comments. The first author would like to express sincere gratitude to the University of Sistan and Baluchestan for its invaluable supports.

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, P.O. Box 397, 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

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  1. Hamid Baghani
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HB and JJN contributed to the mathematical proof and writing the paper. All authors gave final approval for publication. The authors contributed to the mathematical proof and writing the paper. All authors gave final approval for publication.

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Correspondence to Hamid Baghani.

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Baghani, H., Nieto, J.J. Some New Properties of the Mittag-Leffler Functions and Their Applications to Solvability and Stability of a Class of Fractional Langevin Differential Equations. Qual. Theory Dyn. Syst. 23, 18 (2024). https://doi.org/10.1007/s12346-023-00870-4

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