## Table of Content Open Access

ARTICLE

# Three-Variable Shifted Jacobi Polynomials Approach for Numerically Solving Three-Dimensional Multi-Term Fractional-Order PDEs with Variable Coefficients

Jiaquan Xie1,3,*, Fuqiang Zhao1,3, Zhibin Yao1,3, Jun Zhang1,2

College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China.
Taiyuan Institute of China Coal Technology Engineering Group, Taiyuan 030006, China.
Collaborative Innovation Center of Taiyuan Heavy Machinery Equipment, Taiyuan 030024, China.

* Corresponding author: Jiaquan Xie. Email: .

Computer Modeling in Engineering & Sciences 2018, 115(1), 67-84. https://doi.org/10.3970/cmes.2018.115.067

## Abstract

In this paper, the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of three-dimensional multi-term fractional-order PDEs with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. The approximate solutions of nonlinear fractional PDEs with variable coefficients thus obtained by three-variable shifted Jacobi polynomials are compared with the exact solutions. Furthermore some theorems and lemmas are introduced to verify the convergence results of our algorithm. Lastly, several numerical examples are presented to test the superiority and efficiency of the proposed method.

## Keywords

Xie, J., Zhao, F., Yao, Z., Zhang, J. (2018). Three-Variable Shifted Jacobi Polynomials Approach for Numerically Solving Three-Dimensional Multi-Term Fractional-Order PDEs with Variable Coefficients. CMES-Computer Modeling in Engineering & Sciences, 115(1), 67–84. 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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