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A Novel Numerical Method For Solving Fuzzy Variable-Order Differential Equations With Mittag-Leffler Kernels

Author

Listed:
  • HOSSEIN JAFARI

    (Department of Mathematics, University of Mazandaran, Babolsar, Iran†Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa‡Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110122, Taiwan)

  • ROGHAYEH MOALLEM GANJI

    (Department of Mathematics, University of Mazandaran, Babolsar, Iran)

  • DAVOOD DOMIRI GANJI

    (�Department of Mechanical Engineering, Babol University of Technology, Babol, Iran)

  • ZAKIA HAMMOUCH

    (�Division of Applied Mathematics, Thu Dau Mot University Binh Duong Province, Vietnam∥Laboratoire des Systémes Intelligents, Energie et Développement Durable (SIEDD), Faculté des Sciences de l’Ingénieur, Université Privé de Fes, Morocco**Département des Sciences, École Normale Supérieure, Moulay Ismail University of Meknès, Meknes 50000, Morocco)

  • YUSIF S. GASIMOV

    (��†Azerbaijan University, J. Hajibeyli St. 71, AZ1007 Baku, Azerbaijan‡‡Institute of Mathematics and Mechanics, ANAS, B. Vahabzade St. 9, AZ1141 Baku, Azerbaijan§§Institute for Physical Problems, Baku State University, Z. Khalilov St. 23, AZ1148 Baku, Azerbaijan)

Abstract

In the fuzzy calculus, the study of fuzzy differential equations (FDEs) created a proper setting to model real problems which contain vagueness or uncertainties factors. In this paper, we consider a class fuzzy differential equations (FFDEs) with non-integer or variable order (VO). The variable order derivative is defined in the Atangana–Baleanu–Caputo sense on fuzzy set-valued functions. The main problem under the fuzzy initial condition is converted to a new problem by the r-cut representation of fuzzy-valued function. For solving the new problem, we use the operational matrices (OMs) based on the shifted Legendre polynomials (SLPs). By approximating the unknown function and its derivative in terms of the SLPs and substituting these approximations into the equation, the main problem is converted to a system of nonlinear algebraic equations. An error estimate of the numerical solution is proved. Finally, an example is considered to confirm the accuracy of the proposed technique.

Suggested Citation

  • Hossein Jafari & Roghayeh Moallem Ganji & Davood Domiri Ganji & Zakia Hammouch & Yusif S. Gasimov, 2023. "A Novel Numerical Method For Solving Fuzzy Variable-Order Differential Equations With Mittag-Leffler Kernels," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:04:n:s0218348x23400637
    DOI: 10.1142/S0218348X23400637
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