Analytical and numerical solutions of the telegraph equation using the Atangana–Caputo fractional order derivative

Abstract

This paper describes the telegraph equation using the Atangana–Caputo’s fractional derivative with two fractional orders and . The new definition is based on the concept of the power law and the generalized Mittag-Leffler function. The first order of the derivative equation was included in the power law function and the second was included in the generalized Mittag-Leffler function. This approach considers media which have two different properties. The fractional spatial derivative equation and the fractional temporal derivative equation were analyzed separately. The generalization of these equations exhibit different cases of anomalous behavior. Numerical solutions using an iterative scheme were obtained.

Keywords:

• Fractional telegraph equation
• Mittag-Leffler function
• iterative method
• bi-order fractional derivative

Acknowledgements

We would like to thank to Mayra Martínez for the interesting discussions. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jóvenes investigadores 2014.

Notes

No potential conflict of interest was reported by the author.