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Operational Matrix Method for Solving Variable Order Fractional Integro-differential Equations

Mingxu Yi1, Jun Huang1, Lifeng Wang1
1 School of Aeronautic Science and Technology, Beihang University , Beijing, China.

Computer Modeling in Engineering & Sciences 2013, 96(5), 361-377. https://doi.org/10.3970/cmes.2013.096.361

Abstract

In this paper, operational matrix method based upon the Bernstein polynomials is proposed to solve the variable order fractional integro-differential equations in the Caputo derivative sense. We derive the Bernstein polynomials operational matrix of fractional order integration and introduce the product operational matrix of Bernstein polynomials. A truncated the Bernstein polynomials series together with the polynomials operational matrix are utilized to reduce the variable order fractional integro-differential equations to a system of algebraic equations. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Some examples are included to demonstrate the validity and applicability of the method.

Keywords

Bernstein polynomials, variable order fractional, operational matrix, numerical solution.

Cite This Article

Yi, M., Huang, J., Wang, L. (2013). Operational Matrix Method for Solving Variable Order Fractional Integro-differential Equations. CMES-Computer Modeling in Engineering & Sciences, 96(5), 361–377.



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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