Operational method for solving fractional differential equations using cubic B-spline approximation

Abstract

In the present paper we construct the cubic B-spline operational matrix of fractional derivative in the Caputo sense, and use it to solve fractional differential equation. The main characteristic of the approach is that it overcomes the computational difficulty induced by the memory effect. There is no need to save and call all historic information, which can save memory space and reduce computational complexity. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation. The results from this method are good in terms of accuracy.

Keywords:

• Caputo derivative
• cubic B-spline function
• operational matrix of fractional derivative
• interpolating condition
• multi-resolution analysis

2010 AMS Subject Classifications:

• 41A10
• 41A15
• 35C11

Acknowledgements

The author is very grateful to both reviewers and editors of this paper for their constructive comments and nice suggestions which have improved the paper.

This work is supported by the Natural Science Foundation of China under Grant No. 11201240.