A Study of Fuzzy Methods for Solving System of Fuzzy Differential Equations

M. Keshavarz, T. Allahviranloo, S. Abbasbandy and M. H. Modarressi
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M. Keshavarz: 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, Iran2Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
S. Abbasbandy: Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran
M. H. Modarressi: Department of Medical Genetics & Molecular Medicine, Tehran University of Medical Sciences, Tehran, Iran

New Mathematics and Natural Computation (NMNC), 2021, vol. 17, issue 01, 1-27

Abstract: This paper is devoted to obtain an analytical solution for first-order fuzzy differential equations and system of fuzzy differential equations by different methods by considering the type of generalized Hukuhara differentiability of a solution and without embedding them to crisp equations. Moreover, the fuzzy solutions of a second-order fuzzy differential equation by considering the type of differentiability are obtained using reduction to a system of fuzzy differential equations. The effectiveness and efficiency of the approaches are illustrated by solving several practical examples such as Newton’s law of cooling, the mathematical models for the distribution of a drug in the human body and the fuzzy forced harmonic oscillator problem.

Keywords: First-order fuzzy differential equation; system of first-order fuzzy differential equation; generalized Hukuhara differentiability; Newton’s law of cooling; the mathematical models for the distribution of a drug; the fuzzy forced harmonic oscillator problem (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S1793005721500010

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