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International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(2): 144-154
Published online June 25, 2022
https://doi.org/10.5391/IJFIS.2022.22.2.144
© The Korean Institute of Intelligent Systems
Solutions of a System of Fuzzy Fractional Differential in Terms of the Matrix Mittag-Leffler Functions
V. Padmapriya1,2 and M. Kaliyappan3
1Vellore Institute of Technology, Chennai Campus, India
2New Prince Shri Bhavani Arts and Sciences College, Chennai, India
3Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, India
Correspondence to :
V. Padmapriya (v.padmapriya2015@vit.ac.in)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The matrix Mittag-Leffler functions play a crucial role in several applications related to systems with fractional dynamics. These functions represent a generalization for fractional-order systems of the matrix exponential function involved in integer-order systems. Computational techniques for evaluating the matrix Mittag-Leffler functions are therefore of particular importance. In this study, a fuzzy system of differential equations with fractional derivatives was solved in terms of the matrix Mittag-Leffler functions. The matrix Mittag-Leffler function was evaluated based on the Jordan canonical form and the minimal polynomial of the matrix.
Keywords: Mittag-Leffler function, Fuzzy calculus, Fractional calculus, System of fuzzy fractional differential equations, Fractional differential equations
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No potential conflict of interest relevant to this article was reported.
Biographies
E-mail: v.padmapriya2015@vit.ac.in
E-mail: kaliyappan.m@vit.ac.in
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Original Article
International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(2): 144-154
Published online June 25, 2022 https://doi.org/10.5391/IJFIS.2022.22.2.144
Copyright © The Korean Institute of Intelligent Systems.
Solutions of a System of Fuzzy Fractional Differential in Terms of the Matrix Mittag-Leffler Functions
V. Padmapriya1,2 and M. Kaliyappan3
1Vellore Institute of Technology, Chennai Campus, India
2New Prince Shri Bhavani Arts and Sciences College, Chennai, India
3Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, India
Correspondence to:V. Padmapriya (v.padmapriya2015@vit.ac.in)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The matrix Mittag-Leffler functions play a crucial role in several applications related to systems with fractional dynamics. These functions represent a generalization for fractional-order systems of the matrix exponential function involved in integer-order systems. Computational techniques for evaluating the matrix Mittag-Leffler functions are therefore of particular importance. In this study, a fuzzy system of differential equations with fractional derivatives was solved in terms of the matrix Mittag-Leffler functions. The matrix Mittag-Leffler function was evaluated based on the Jordan canonical form and the minimal polynomial of the matrix.
Keywords: Mittag-Leffler function, Fuzzy calculus, Fractional calculus, System of fuzzy fractional differential equations, Fractional differential equations
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