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Existence and Stability Analysis of Solution for Mathieu Fractional Differential Equations with Applications on Some Physical Phenomena

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Abstract

This paper deals with a class of nonlinear Mathieu fractional differential equations. The reported results discuss the existence, uniqueness and stability for the solution of proposed equation. We prove the main results by the aid of fixed point theorems and Ulam’s approach. The paper is appended with two applications that describe the force of periodic pendulum and the motion of a particle in the plane. Graphical representations are used to illustrate the results.

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Funding

J. Alzabut would like to thank Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RGDES-2017-01-17.

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Authors and Affiliations

  1. Department of Mathematics, 08 May 1945 University-Guelma, Guelma, Algeria

    N. Tabouche & A. Berhail

  2. Department of Mathematics, Al-Azhar University-Gaza, Gaza, State of Palestine

    M. M. Matar

  3. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

    J. Alzabut

  4. Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Tamil Nadu, 635 601, India

    A. G. M. Selvam & D. Vignesh

Authors
  1. N. Tabouche
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  2. A. Berhail
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  3. M. M. Matar
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  4. J. Alzabut
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  5. A. G. M. Selvam
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  6. D. Vignesh
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Contributions

All authors have contributed equally and significantly to this paper. All authors have read and approved the final version of the manuscript.

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Correspondence to J. Alzabut.

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Tabouche, N., Berhail, A., Matar, M.M. et al. Existence and Stability Analysis of Solution for Mathieu Fractional Differential Equations with Applications on Some Physical Phenomena. Iran J Sci Technol Trans Sci 45, 973–982 (2021). https://doi.org/10.1007/s40995-021-01076-6

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  • DOI: https://doi.org/10.1007/s40995-021-01076-6

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