Numerical Investigation of Ordinary and Partial Differential Equations with Variable Fractional Order by Bernstein Operational Matrix
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Date
2022
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Springer
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Abstract
This research proposes a method to find numerical solutions of the variable-order fractional differential equation. We derived new operational matrix by applying Bernstein polynomials. Then, using this matrix, the method of solving the system of variable-order fractional differential equation and variable-order fractional partial differential equation are presented. Various numerical examples of these problems are provided along with the figures and tables. Finally, the accuracy of the proposed method is evaluated. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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Keywords
Bernstein Polynomials, Operational Matrix, Partial Differential Equation Problems, Riemann-Liouville Fractional Derivative And Integral, System Of Nonlinear Differential Equations Problems, Variable Order Fractional Differential Equations
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Citation
Taleshian, Amir Hose;...et.al. (2022). "Numerical Investigation of Ordinary and Partial Differential Equations with Variable Fractional Order by Bernstein Operational Matrix", International Journal of Applied and Computational Mathematics, Vol.8, No.6.
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International Journal of Applied and Computational Mathematics
Volume
8
Issue
6