An Efficient Numerical Method for Fractional Differential Equations with Two Caputo Derivatives

Authors

  • Shuiping Yang Department of Mathematics, Huizhou University, Guangdong, 516007, China
  • Aiguo Xiao School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China.

DOI:

https://doi.org/10.4208/jcm.1510-m2014-0050

Keywords:

Fractional differential equations, Caputo derivatives, Spline collocation method, Convergence, Stability.

Abstract

In this paper, we study the Hermite cubic spline collocation method with two parameters for solving an 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.

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Published

2018-08-22

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Issue

Vol. 34 No. 2 (2016)

Section

Articles

How to Cite

An Efficient Numerical Method for Fractional Differential Equations with Two Caputo Derivatives. (2018). Journal of Computational Mathematics, 34(2), 113-134. https://doi.org/10.4208/jcm.1510-m2014-0050