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 - <p style="text-align: justify;">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.</p>