Math. Model. Nat. Phenom.
Volume 12, Number 6, 2017Special Issue - Nonlocal and delay equations
|Page(s)||51 - 67|
|Published online||30 December 2017|
The neutral-fractional telegraph equation
Department of Mathematics, Faculty of Science, Kuwait University,
2 Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences Berlin, Luxemburger Str. 10, 13353 Berlin, Germany
Accepted: 12 September 2017
In this paper, the neutral-fractional telegraph equation is introduced and discussed. This equation is a natural fractional generalization of the conventional telegraph equation and contains two time-fractional Caputo derivatives of the orders α and α∕2, respectively, and the Riesz space-fractional derivative of the order α, 1 < α ≤ 2. In this paper, we derive some analytical representations of the fundamental solution to this equation and discuss its properties. A special focus is put to two prominent particular cases of the neutral-fractional telegraph equation, namely, to the α-fractional wave equation and to the α-fractional diffusion equation that contain only one time-fractional Caputo derivative of the order α or α∕2, respectively.
Mathematics Subject Classification: 26A33 / 35C05 / 35E05 / 35L05 / 45K05 / 60E99
Key words: Neutral-fractional telegraph equation / α-fractional wave equation / α-fractional diffusion equation / fundamental solution / probability density function / entropy production rate
© EDP Sciences, 2017
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