Numerical Study for a Class of Variable Order Fractional Integral-differential Equation in Terms of Bernstein Polynomials
Jinsheng Wang, Liqing Liu, Yiming Chen, Lechun Liu and Dayan Liu

doi:10.3970/cmes.2015.104.069
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 104, No. 1, pp. 69-85, 2015
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Keywords Bernstein polynomials, variable order fractional integral-differential equation, operational matrix, numerical solution, convergence analysis, the absolute error.
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.

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