An efficient cubic spline approximation for variable-order fractional differential equations with time delay

作者：Yaghoobi Shole; Moghaddam Behrouz Parsa^*; Ivaz Karim

来源：Nonlinear Dynamics, 2017, 87(2): 815-826.

DOI：10.1007/s11071-016-3079-4

• Fractional calculus
• Variable-order derivative
• Spline approximation
• Functional differential equations
• Oscillatory dynamic systems

This paper describes a robust, accurate and efficient scheme based on a cubic spline interpolation. The proposed scheme is applied to approximate variable-order fractional integrals and is extended to solve a class of nonlinear variable-order fractional equations with delay. Modified Hutchinson equation and delay Ikeda equation are solved using the proposed scheme. The efficiency and accuracy of the proposed method are analyzed in the perspective of the mean absolute error and experimental convergence order. Numerical results confirm the accuracy and efficiency of the proposed scheme.

• 出版日期2017-1