Using reproducing kernel for solving a class of time-fractional telegraph equation with initial value conditions

ABSTRACT

Today, most of the real physical world problems can be best modelled with fractional telegraph equation. Besides modelling, the solution techniques and their reliability are the most important. Therefore, high accuracy solutions are always needed. As we all know, reproducing kernel method (RKM) has been successfully presented for solving various ordinary differential equations. However, the numerical results are not perfectly satisfactory when we directly use the traditional RKM for solving fractional partial differential equation. The aim of this paper is to fill this gap. In this paper, a new method is provided for solving fractional telegraph equation in the reproducing kernel space by piecewise technique, which can obtain more accurate solution than traditional method. Three experiments are given to demonstrate the effectiveness of the present method.

KEYWORDS:

• Piecewise
• reproducing kernel space
• fractional telegraph equation
• Caputo fractional derivative

2000 AMS SUBJECT CLASSIFICATIONS:

• 41A30
• 26A33
• 49K20

Acknowledgements

The authors would like to express their thanks to the reviewers for their careful reading and helpful comments.

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 [grant number 11361037], the Natural Science Foundation of Inner Mongolia [grant number 2017MS01], [grant number 2015MS0118], Project Application Technology Research and Development Foundation of Inner Mongolia [grant number 20120312].