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Title
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A NOVEL NUMERICAL METHOD FOR SOLVING FUZZY VARIABLE-ORDER DIFFERENTIAL EQUATIONS WITH MITTAG-LEFFLER KERNELS
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Type
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JournalPaper
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Keywords
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Atangana–Baleanu–Caputo Derivative; Fixed and Variable Order; Fuzzy Fractional Differential Equations; The Shifted Legendre Polynomials; Operational Matrix
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Abstract
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In the fuzzy calculus, the study of fuzzy differential equations (FDEs) created a proper setting to model real problems which contain vagueness or uncertainties factors. In this paper, we consider a class fuzzy differential equations (FFDEs) with non-integer or variable order (VO). The variable order derivative is defined in the Atangana–Baleanu–Caputo sense on fuzzy setvalued functions. The main problem under the fuzzy initial condition is converted to a new problem by the r-cut representation of fuzzy-valued function. For solving the new problem, we use the operational matrices (OMs) based on the shifted Legendre polynomials (SLPs). By approximating the unknown function and its derivative in terms of the SLPs and substituting these approximations into the equation, the main problem is converted to a system of nonlinear algebraic equations. An error estimate of the numerical solution is proved. Finally, an example is considered to confirm the accuracy of the proposed technique
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Researchers
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YUSIF S GASIMOV (Fifth Researcher), Zakia Hammouch (Fourth Researcher), D D Ganji (Third Researcher), Roghayeh Moallem Ganji (Second Researcher), Hossein Jafari (First Researcher)
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