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A study of the time-fractional heat equation under the generalized Hukuhara conformable fractional derivative

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  • Eghlimi, Hadi
  • Asgari, Mohammad Sadegh

Abstract

In this article, we address the dual challenges posed by the complexities of fractional calculus and fuzzy uncertainty in mathematical modeling, with a specific focus on the time-fractional heat equation. We introduce a novel concept, the partial generalized Hukuhara conformable fractional derivative, as a bridge between these domains. Complementing this concept, we develop a unique fuzzy tϑϑ-Laplace transform, which enables efficient problem-solving. This transformative approach, coupled with the fuzzy Fourier transform, provides a novel method for deriving fundamental fuzzy solutions for the time-fractional heat equation. We substantiate our approach through successful examples, highlighting its efficacy in complex scenarios. This study pioneers an innovative methodology that unites fractional calculus and fuzzy logic, opening new avenues for addressing real-world challenges.

Suggested Citation

  • Eghlimi, Hadi & Asgari, Mohammad Sadegh, 2023. "A study of the time-fractional heat equation under the generalized Hukuhara conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923009086
    DOI: 10.1016/j.chaos.2023.114007
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    References listed on IDEAS

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    1. Najariyan, Marzieh & Qiu, Li, 2023. "Singular fuzzy fractional quadratic regulator problem," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
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    4. Al-Smadi, Mohammed & Arqub, Omar Abu & Zeidan, Dia, 2021. "Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Martynyuk, Anatoliy A. & Stamov, Gani Tr. & Stamova, Ivanka M., 2020. "Fractional-like Hukuhara derivatives in the theory of set-valued differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Atimad Harir & Said Melliani & Lalla Saadia Chadli, 2021. "Fuzzy Conformable Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-6, February.
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