On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation
نویسنده
چکیده
In this paper, some new properties of the fundamental solution to the multi-dimensional 1 spaceand time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes 2 representation of the fundamental solution that was derived in the previous publications of the 3 author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution 4 in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new 5 closed form formulas for particular cases of the fundamental solution are derived. In particular, 6 we solve an open problem of representation of the fundamental solution to the two-dimensional 7 neutral-fractional diffusion-wave equation in terms of the known special functions. 8
منابع مشابه
An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation
Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...
متن کاملExact solutions of distinct physical structures to the fractional potential Kadomtsev-Petviashvili equation
In this paper, Exp-function and (G′/G)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. As a results, some new exact traveling wave solutions are obtained.
متن کاملA new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics
In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...
متن کاملWave Propagation and Fundamental Solution of Initially Stressed Thermoelastic Diffusion with Voids
The present article deals with the study of propagation of plane waves in isotropic generalized thermoelastic diffusion with voids under initial stress. It is found that, for two dimensional model of isotropic generalized thermoelastic diffusion with voids under initial stress, there exists four coupled waves namely, P wave, Mass Diffusion (MD) wave, thermal (T) wave and Volume Fraction (VF) wa...
متن کاملNumerical Solution of Space-time Fractional two-dimensional Telegraph Equation by Shifted Legendre Operational Matrices
Fractional differential equations (FDEs) have attracted in the recent years a considerable interest due to their frequent appearance in various fields and their more accurate models of systems under consideration provided by fractional derivatives. For example, fractional derivatives have been used successfully to model frequency dependent damping behavior of many viscoelastic materials. They a...
متن کامل