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On Numerical And Theoretical Findings For Fractal-Fractional Order Generalized Dynamical System

Author

Listed:
  • HAIDONG QU

    (Department of Mathematics, Hanshan Normal University, Chaozhou 515041, P. R. China)

  • MUHAMMAD ARFAN

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

  • KAMAL SHAH

    (Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan†Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia)

  • AMAN ULLAH

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

  • THABET ABDELJAWAD

    (��Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia‡Department of Medical Research, China Medical University, Taichung 40402, Taiwan§Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea¶Department of Computer Science and Technology, Hanshan Normal University, ChaoZhou, Guangdong 521041, P. R. China)

  • GENGZHONG ZHANG

    (�Department of Computer Science and Technology, Hanshan Normal University, ChaoZhou, Guangdong 521041, P. R. China)

Abstract

In this paper, we consider a general system of fractal-fractional order derivative in Atangana–Baleanu–Caputo sense. On the application of fixed point approach, we establish sufficient conditions regarding existence and uniqueness of solution. The said requirements are obtained via using Krasnoselkii’s and Banach fixed results. Further via nonlinear analysis, some interesting results for Hyers–Ulam (HU)-type stability are also derived. To compute numerical solution for the proposed nonlinear system, fractal-fractional order Adams–Bashforth method is used. To support our findings, we give some test problems. Also by Matlab, we also present their graphical interpretation. The analysis of this paper is in generalized format which can be applied to any real problem. Each equation is investigated separately for the said characteristics.

Suggested Citation

  • Haidong Qu & Muhammad Arfan & Kamal Shah & Aman Ullah & Thabet Abdeljawad & Gengzhong Zhang, 2023. "On Numerical And Theoretical Findings For Fractal-Fractional Order Generalized Dynamical System," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-19.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:02:n:s0218348x23400194
    DOI: 10.1142/S0218348X23400194
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