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AIMS Mathematics

2023, Volume 8, Issue 11: 27840-27856. doi: 10.3934/math.20231424
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Research article

Stability analysis of new generalized mean-square stochastic fractional differential equations and their applications in technology

  • 1.
    Directorate General of Commerce Education and Management Sciences, Higher Education Department, Peshawar, Pakistan
  • 2.
    College of Engineering and IT, University of Dubai, UAE
  • Received: 16 July 2023 Revised: 16 September 2023 Accepted: 25 September 2023 Published: 09 October 2023

  • MSC : 34A08, 34B15, 34B27

  • Stability theory has significant applications in technology, especially in control systems. On the other hand, the newly defined generalized mean-square stochastic fractional (GMSF) operators are particularly interesting in control theory and systems due to their various controllable parameters. Thus, the combined study of stability theory and GMSF operators becomes crucial. In this research work, we construct a new class of GMSF differential equations and provide a rigorous proof of the existence of their solutions. Furthermore, we investigate the stability of these solutions using the generalized Ulam-Hyers-Rassias stability criterion. Some examples are also provided to demonstrate the effectiveness of the proposed approach in solving fractional differential equations (FDEs) and evaluating their stability. The paper concludes by discussing potential applications of the proposed results in technology and outlining avenues for future research.

    Citation: Tahir Ullah Khan, Christine Markarian, Claude Fachkha. Stability analysis of new generalized mean-square stochastic fractional differential equations and their applications in technology[J]. AIMS Mathematics, 2023, 8(11): 27840-27856. doi: 10.3934/math.20231424

    Related Papers:

  • Stability theory has significant applications in technology, especially in control systems. On the other hand, the newly defined generalized mean-square stochastic fractional (GMSF) operators are particularly interesting in control theory and systems due to their various controllable parameters. Thus, the combined study of stability theory and GMSF operators becomes crucial. In this research work, we construct a new class of GMSF differential equations and provide a rigorous proof of the existence of their solutions. Furthermore, we investigate the stability of these solutions using the generalized Ulam-Hyers-Rassias stability criterion. Some examples are also provided to demonstrate the effectiveness of the proposed approach in solving fractional differential equations (FDEs) and evaluating their stability. The paper concludes by discussing potential applications of the proposed results in technology and outlining avenues for future research.


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