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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

APA Style
Yi, M., Huang, J., Wang, L. (2013). Operational matrix method for solving variable order fractional integro-differential equations. Computer Modeling in Engineering & Sciences, 96(5), 361-377. https://doi.org/10.3970/cmes.2013.096.361
Vancouver Style
Yi M, Huang J, Wang L. Operational matrix method for solving variable order fractional integro-differential equations. Comput Model Eng Sci. 2013;96(5):361-377 https://doi.org/10.3970/cmes.2013.096.361
IEEE Style
M. Yi, J. Huang, and L. Wang "Operational Matrix Method for Solving Variable Order Fractional Integro-differential Equations," Comput. Model. Eng. Sci., vol. 96, no. 5, pp. 361-377. 2013. https://doi.org/10.3970/cmes.2013.096.361

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