• Original Articles •

### AN EFFICIENT NUMERICAL METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO CAPUTO DERIVATIVES

Shuiping Yang1, Aiguo Xiao2

1. 1. Department of Mathematics, Huizhou University, Guangdong, 516007, China;
2. School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan, 411105, China
• Received:2014-09-05 Revised:2015-10-21 Online:2016-03-15 Published:2016-03-15
• Supported by:

This work is supported by projects from the National NSF of China (Grant No. 11501238, Grant No. 11401248), NSF of Guangdong Province (Grant No. 2014A-030313641), and NSF of Huizhou University (Grant No. hzuxl201420). The authors are very grateful to the reviewers for their useful comments.

Shuiping Yang, Aiguo Xiao. AN EFFICIENT NUMERICAL METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO CAPUTO DERIVATIVES[J]. Journal of Computational Mathematics, 2016, 34(2): 113-134.

In this paper, we study the Hermite cubic spline collocation method with two parameters for solving a initial value problem (IVP) of nonlinear fractional differential equations with two Caputo derivatives. The convergence and nonlinear stability of the method are established. Some illustrative examples are provided to verify our theoretical results. The numerical results also indicate that the convergence order is min{4 ? α, 4 ? β}, where 0 < β < α < 1 are two parameters associated with the fractional differential equations. Mathematics subject classi cation: 65L20, 65L60, 34A08.

CLC Number:

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