 Open Access

ARTICLE

# 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.

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.

View

• ### 0

Like

Related articles
• Mingxu Yi, Jun Huang, Lifeng Wang   