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Solving variable-order fractional differential algebraic equations via generalized fuzzy hyperbolic model with application in electric circuit modeling

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Abstract

In this paper, a new approach based on a generalized fuzzy hyperbolic model is used for the numerical solution of variable-order fractional differential algebraic equations. The fractional derivative is described in the Atangana–Baleanu sense that is a new derivative with fractional order based on the generalized Mittag–Leffler function. First, by using fuzzy solutions with adjustable parameters, the variable-order fractional differential algebraic equations are reduced to a problem consisting of solving a system of algebraic equations. For adjusting the parameters of fuzzy solutions, an unconstrained optimization problem is then considered. A learning algorithm is also presented for solving the unconstrained optimization problem. Finally, some numerical examples are given to verify the efficiency and accuracy of the proposed approach.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran

    Marzieh Mortezaee, Mehdi Ghovatmand & Alireza Nazemi

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  1. Marzieh Mortezaee
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  2. Mehdi Ghovatmand
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  3. Alireza Nazemi
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Correspondence to Mehdi Ghovatmand.

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Mortezaee, M., Ghovatmand, M. & Nazemi, A. Solving variable-order fractional differential algebraic equations via generalized fuzzy hyperbolic model with application in electric circuit modeling. Soft Comput 24, 16745–16758 (2020). https://doi.org/10.1007/s00500-020-04969-7

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