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Analytical solution for a generalized space-time fractional telegraph equation

Ahmad Fino 1, 2, Hassan Ibrahim 2

(2011-06-01)

In this paper, we consider a nonhomogeneous space-time fractional telegraph equation defined in a bounded space domain, which is obtained from the standard telegraph equation by replacing the first- or second-order time derivative by the Caputo fractional derivative $D^\alpha_t$, $\alpha>0$; and the Laplacian operator by the fractional Laplacian $(-\Delta)^{\beta/2}$, $\beta\in(0,2]$. We discuss and derive the analytical solutions under nonhomogeneous Dirichlet and Neumann boundary conditions by using the method of separation of variables. The obtained solutions are expressed through multivariate Mittag-Leffler type functions. Special cases of solutions are also discussed.

1:	Laboratoire de mathématiques et applications (LaMA--Liban)
	Université Libanaise
2:	Lebanese International University (LIU)
	Lebanese International University

Subject

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Mathematics/Analysis of PDEs

Keyword(s): Fractional telegraph equation – Fractional Laplacian – Caputo fractional derivative – Multivariate Mittag-Leffler type functions – Method of separating variables

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From: Ahmad Fino <>

Submitted on: Sunday, 7 August 2011 00:52:15

Updated on: Sunday, 7 August 2011 18:21:35