Issue |
Math. Model. Nat. Phenom.
Volume 12, Number 6, 2017
Special Issue - Nonlocal and delay equations
|
|
---|---|---|
Page(s) | 51 - 67 | |
DOI | https://doi.org/10.1051/mmnp/2017064 | |
Published online | 30 December 2017 |
The neutral-fractional telegraph equation
1
Department of Mathematics, Faculty of Science, Kuwait University,
13060
Safat, Kuwait
2
Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences Berlin,
Luxemburger Str. 10,
13353
Berlin, Germany
Received:
11
September
2017
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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