Numerical Method to Solve a Hybrid Fuzzy Conformable Fractional Differential Equations

N. Shahryari, T. Allahviranloo and S. Abbasbandy
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N. Shahryari: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
T. Allahviranloo: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran†Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
S. Abbasbandy: Department of Mathematics, Imam Khomeini International University, Qazvin, 34149 16818, Iran

New Mathematics and Natural Computation (NMNC), 2022, vol. 18, issue 03, 629-655

Abstract: This research introduces a new definition of fuzzy fractional derivative, fuzzy conformable fractional derivative, which is defined based on generalized Hukuhara differentiability. Namely, we investigate the Hybrid fuzzy fractional differential equation with the fuzzy conformable fractional generalized Hukuhara derivative. We establish that the Hybrid fuzzy fractional differential equation admits two fuzzy triangular solutions and prove that these fuzzy solutions are obtained together with a characterization of these solutions by two systems of fractional differential equations. We propose an adaptable numerical scheme for the approximation of the fuzzy triangular solutions. Numerical results reveal that the numerical method is convenient for solving the Hybrid fuzzy conformable fractional differential equation.

Keywords: Generalized Hukuhara conformable fractional derivative; hybrid fuzzy conformable fractional differential equation; Müntz–Legendre wavelet method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S1793005722500326

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