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# Legendre Polynomials Method for Solving a Class of Variable Order Fractional Differential Equation

Lifeng Wang1, Yunpeng Ma1,2, Yongqiang Yang1

School of Aeronautic Science and Technology, Beihang University, Beijing, China.
Corresponding author.

Computer Modeling in Engineering & Sciences 2014, 101(2), 97-111. https://doi.org/10.3970/cmes.2014.101.097

## Abstract

In this paper, a numerical method based on the Legendre polynomials is presented for a class of variable order fractional differential equation. We adopt the Coimbra variable order fractional operator, which can be viewed as a Caputo-type definition. Three different kinds of operational matrixes with Legendre polynomials are derived. A truncated the Legendre polynomials series together with the products of several dependent matrixes are utilized to reduce the variable order fractional differential equation to a system of algebraic equations. The solution of this system gives the approximation solution for the truncated limited n. An error analysis technique is also given. Some examples are included to demonstrate the validity and applicability of the approach.

## Keywords

APA Style
Wang, L., Ma, Y., Yang, Y. (2014). Legendre polynomials method for solving a class of variable order fractional differential equation. Computer Modeling in Engineering & Sciences, 101(2), 97-111. https://doi.org/10.3970/cmes.2014.101.097
Vancouver Style
Wang L, Ma Y, Yang Y. Legendre polynomials method for solving a class of variable order fractional differential equation. Comput Model Eng Sci. 2014;101(2):97-111 https://doi.org/10.3970/cmes.2014.101.097
IEEE Style
L. Wang, Y. Ma, and Y. Yang "Legendre Polynomials Method for Solving a Class of Variable Order Fractional Differential Equation," Comput. Model. Eng. Sci., vol. 101, no. 2, pp. 97-111. 2014. https://doi.org/10.3970/cmes.2014.101.097

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