Two-Dimensional Müntz–Legendre Wavelet Method for Fuzzy Hybrid 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, Istinye University, Istanbul, Turkey
S. Abbasbandy: ��Department of Mathematics, Imam Khomeini International University, Qazvin 34149-16818, Iran

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 01, 173-193

Abstract: In this paper, the fuzzy approximate solutions for the fuzzy Hybrid differential equation emphasizing the type of generalized Hukuhara differentiability of the solutions are obtained by using the two-dimensional Müntz–Legendre wavelet method. To do this, the fuzzy Hybrid differential equation is transformed into a system of linear algebraic equations in a matrix form. Thus, by solving this system, the unknown coefficients are obtained. The convergence of the proposed method is established in detail. Numerical results reveal that the two-dimensional Müntz–Legendre wavelet is very effective and convenient for solving the fuzzy Hybrid differential equation.

Keywords: Fuzzy hybrid differential equation; two-dimensional Müntz–Legendre wavelet method; generalized Hukuhara differentiable; fuzzy number valued functions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005723500059

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