Time-fractional telegraph equation of distributed order in higher dimensions

被引：17
|
作者：
Vieira, N. [1 ]
Rodrigues, M. M. [1 ]
Ferreira, M. [1 ,2 ]
机构：
[1] Univ Aveiro, CIDMA Ctr Res & Dev Math & Applicat, Dept Math, Campus Univ Santiago, P-3810193 Aveiro, Portugal
[2] Polytech Leiria, Sch Technol & Management, Campus 2 Morro Lena, P-2411901 Alto Do Vieiro, Leiria, Portugal
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2021年 / 102卷
关键词：
Time-fractional telegraph equation; Distributed order; Laplace transform; Fourier transform; Mellin transform; Fox H-functions; Fractional moments; Tauberian Theorem; DIFFUSION-WAVE;
D O I：
10.1016/j.cnsns.2021.105925
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in R-n x R+ is considered. By employing the technique of the Fourier, Laplace and Mellin transforms, a representation of the fundamental solution of this equation in terms of convolutions involving the Fox H-function is obtained. Some particular choices of the density functions in the form of elementary functions are studied. Fractional moments of the fundamental solution are computed in the Laplace domain. Finally, by application of the Tauberian theorems we study the asymptotic behaviour of the second-order moment (variance) in the time domain. (C) 2021 Elsevier B.V. All rights reserved.
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页数：32
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