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Volume 34, Issue 2
An Efficient Numerical Method for Fractional Differential Equations with Two Caputo Derivatives

Shuiping Yang & Aiguo Xiao

DOI: 10.4208/jcm.1510-m2014-0050

J. Comp. Math., 34 (2016), pp. 113-134.

Published online: 2016-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65L20, 65L60, 34A08.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yang52053052@163.com (Shuiping Yang)

xag@xtu.edu.cn (Aiguo Xiao)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-113, author = {Yang , Shuiping and Xiao , Aiguo}, title = {An Efficient Numerical Method for Fractional Differential Equations with Two Caputo Derivatives}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {2}, pages = {113--134}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1510-m2014-0050}, url = {http://global-sci.org/intro/article_detail/jcm/9786.html} }
TY - JOUR T1 - An Efficient Numerical Method for Fractional Differential Equations with Two Caputo Derivatives AU - Yang , Shuiping AU - Xiao , Aiguo JO - Journal of Computational Mathematics VL - 2 SP - 113 EP - 134 PY - 2016 DA - 2016/04 SN - 34 DO - http://doi.org/10.4208/jcm.1510-m2014-0050 UR - https://global-sci.org/intro/article_detail/jcm/9786.html KW - Fractional differential equations, Caputo derivatives, Spline collocation method, Convergence, Stability. AB -

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.

Yang , Shuiping and Xiao , Aiguo. (2016). An Efficient Numerical Method for Fractional Differential Equations with Two Caputo Derivatives. Journal of Computational Mathematics. 34 (2). 113-134. doi:10.4208/jcm.1510-m2014-0050
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