Eur. Phys. J. Special Topics 226, 3693–3703 (2017)
https://doi.org/10.1140/epjst/e2018-00088-6

Regular Article

Numerical solution of fractional telegraph differential equations by theta-method

¹ Harran University, Faculty of Arts and Sciences, Department of Mathematics, Şanl"i"urfa, Turkey
² Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey

^a e-mail: aliakgul00727@gmail.com

Received: 7 October 2017
Received in final form: 19 January 2018
Published online: 25 July 2018

Abstract

Difference schemes for theta method are constructed. Theta method is used to deal with fractional telegraph differential equation defined by Caputo fractional derivative for different values of θ = 0.1, 0.5, 0.9 and fractional orders α = 0.05, 0.1, 0.5, 0.9, 0.95. The stability of difference schemes for this problem is proved by matrix method and the stability of the exact solution is also given. Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the proposed method.