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A novel approach to approximate fractional derivative with uncertain conditions

Author

Listed:
  • Ahmadian, A.
  • Salahshour, S.
  • Ali-Akbari, M.
  • Ismail, F.
  • Baleanu, D.

Abstract

This paper focuses on providing a new scheme to find the fuzzy approximate solution of fractional differential equations (FDEs) under uncertainty. The Caputo-type derivative base on the generalized Hukuhara differentiability is approximated by a linearization formula to reduce the corresponding uncertain FDE to an ODE under fuzzy concept. This new approach may positively affect on the computational cost and easily apply for the other types of uncertain fractional-order differential equation. The performed numerical simulations verify the proficiency of the presented scheme.

Suggested Citation

  • Ahmadian, A. & Salahshour, S. & Ali-Akbari, M. & Ismail, F. & Baleanu, D., 2017. "A novel approach to approximate fractional derivative with uncertain conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 68-76.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:68-76
    DOI: 10.1016/j.chaos.2017.07.026
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    References listed on IDEAS

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    1. Chalco-Cano, Y. & Román-Flores, H., 2008. "On new solutions of fuzzy differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 112-119.
    2. Dumitru Baleanu & Octavian G. Mustafa & Ravi P. Agarwal, 2010. "Asymptotically Linear Solutions for Some Linear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-8, December.
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    Cited by:

    1. Ahmed Salem & Noorah Mshary, 2020. "On the Existence and Uniqueness of Solution to Fractional‐Order Langevin Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    2. MohammadHossein Derakhshan, 2021. "A Numerical Scheme Based on the Chebyshev Functions to Find Approximate Solutions of the Coupled Nonlinear Sine‐Gordon Equations with Fractional Variable Orders," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).
    3. HuiChol Choi & SungHyok Kwon & Kinam Sin & Sunae Pak & Sungryol So, 2019. "Constructive Existence of (1,1)‐Solutions to Two‐Point Value Problems for Fuzzy Linear Multiterm Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2019(1).
    4. Zhao, Lingdong & Chen, Yonghong, 2022. "Comments on “a novel approach to approximate fractional derivative with uncertain conditions”," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. M. Bishehniasar & S. Salahshour & A. Ahmadian & F. Ismail & D. Baleanu, 2017. "An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations," Complexity, Hindawi, vol. 2017, pages 1-12, December.
    6. Salahshour, Soheil & Ahmadian, Ali & Allahviranloo, Tofigh, 2021. "A new fractional dynamic cobweb model based on nonsingular kernel derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Fu, Chao & Zheng, Zhaoli & Zhu, Weidong & Lu, Kuan & Yang, Yongfeng, 2022. "Non-intrusive frequency response analysis of nonlinear systems with interval uncertainty: A comparative study," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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