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Numerical Study for a Class of Variable Order Fractional Integral-differential Equation in Terms of Bernstein Polynomials

Jinsheng Wang1, Liqing Liu2, Yiming Chen2, Lechun Liu2, Dayan Liu3
School of Continuing Education, Yanshan University, Qinhuangdao, 066004, Hebei, China.
College of Science, Yanshan University, Qinhuangdao, 066004, Hebei, China.
INSA Centre Val de Loire, Université d’Orléans, PRISME EA 4229, Bourges 18022 France.

Computer Modeling in Engineering & Sciences 2015, 104(1), 69-85. https://doi.org/10.3970/cmes.2015.104.069

Abstract

The aim of this paper is to seek the numerical solution of a class of variable order fractional integral-differential equation in terms of Bernstein polynomials. The fractional derivative is described in the Caputo sense. Four kinds of operational matrixes of Bernstein polynomials are introduced and are utilized to reduce the initial equation to the solution of algebraic equations after dispersing the variable. By solving the algebraic equations, the numerical solutions are acquired. The method in general is easy to implement and yields good results. Numerical examples are provided to demonstrate the validity and applicability of the method.

Keywords

Bernstein polynomials, variable order fractional integral-differential equation, operational matrix, numerical solution, convergence analysis, the absolute error.

Cite This Article

Wang, J., Liu, L., Chen, Y., Liu, L., Liu, D. (2015). Numerical Study for a Class of Variable Order Fractional Integral-differential Equation in Terms of Bernstein Polynomials. CMES-Computer Modeling in Engineering & Sciences, 104(1), 69–85.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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