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Qualitative Analysis of Fractional Stochastic Differential Equations with Variable Order Fractional Derivative

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Abstract

This research paper has been dedicated to the investigation of Coupled System of Fractional Stochastic Differential Equations (CSFSDEs), which is an extension of Fractional Stochastic Differential equations, an emerging field that is in a developmental stage and demands the focused attention of experts. Within this context, the research article is mainly focused on determining solutions for CSFSDEs featuring variable order derivatives. This article will lay the foundation for establishing the necessary conditions for the existence and uniqueness of the considered CSFSDEs. To achieve this, we have employed Picard’s iteration techniques, which have proven effective in this domain. Furthermore, we will set the groundwork for defining conditions of Ulam’s type stabilities specific to the proposed model. To conclude this work, we have presented an illustrative example that serves to explain the primary findings of our research.

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Acknowledgements

Kamal Shah and Thabet Abdeljawad are thankful to Prince Sultan University for support through the TAS research lab.

Funding

This research paper received no external funding.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Swat, Khyber, Pakhtunkhwa, Pakistan

    Amjad Ali, Khezer Hayat & Abrar Zahir

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

    Kamal Shah & Thabet Abdeljawad

  3. Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber, Pakhtunkhwa, 18000, Pakistan

    Kamal Shah

  4. Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

    Thabet Abdeljawad

  5. Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

    Thabet Abdeljawad

  6. Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Republic of Korea

    Thabet Abdeljawad

Authors
  1. Amjad Ali
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  2. Khezer Hayat
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  3. Abrar Zahir
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  4. Kamal Shah
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  5. Thabet Abdeljawad
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Contributions

Amajad Ali: Played a role in research article, generating new problem ideas, devising problem-solving methods, and reviewing literature. Khezer Hayat: Applied statistical techniques and contributed to solving the main problem. Abrar Zahir: Responsible for writing, reviewing, editing, and submitting the initial draft. Kamal Shah: Provided the core problem idea and contributed to draft review. Thabet Abdeljawad: Edited the revised version and contributed with equal enthusiasm and dedication.

Corresponding authors

Correspondence to Abrar Zahir or Thabet Abdeljawad.

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Ali, A., Hayat, K., Zahir, A. et al. Qualitative Analysis of Fractional Stochastic Differential Equations with Variable Order Fractional Derivative. Qual. Theory Dyn. Syst. 23, 120 (2024). https://doi.org/10.1007/s12346-024-00982-5

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