Using the iterative reproducing kernel method for solving a class of nonlinear fractional differential equations

ABSTRACT

In previous works, we have devoted to using the reproducing kernel methods solving integer order differential equations, based on the review of previous works, in this paper, we mainly present a method for solving a class of higher order fractional differential equations with general boundary value problems by using Taylor formula into reproducing kernel space. Its analytical solution is represented in the form of series. The analytical solution and approximate solution obtained by this method is given and it is uniformly converge to the exact solution and its corresponding derivatives. The numerical examples are studied to demonstrate the accuracy of the present method.

Keywords:

• Taylor formula
• boundary value problems
• reproducing kernel Hilbert space
• singular-coefficient
• fractional differential equations

2017 AMS SUBJECT CLASSIFICATIONS:

• 34K28
• 34K07
• 34B10

Acknowledgments

We thank the reviewer for their valuable suggestions, which greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper is supported by the National Natural Science Foundation of China (no. 11361037), the Natural Science Foundation of Inner Mongolia (no. 2015MS0118).