Multidimensional solutions of time-fractional diffusion-wave equations

By Andrzej Hanygad. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2002

160 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/158dcce12ae0d6d741e3f3ee03c6647cf4fc20f4

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Citations in the corpus

Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations (2009, methodology): “(b ) Solution kernel of the distributed diffusion-wave equation Similarly, as was carried out by Hanyga (2002b), Kochubei (2008) and Mainardi et al. (2008), we use (3.12) to obtain a solution kernel.”
Boundary value problems for multi-term fractional differential equations (2008, methodology): “There exists a large number of articles devoted to the study of one-dimensional anomalous diffusion [1–9], whereas a few have discussed multi-dimensional case [1,10].”
Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution (2007, background): “In this way, a FPDE which received much attention in the literature is that one obtained by substituting fractional derivatives for the time derivative and the space derivative in the diusion equation [1,2,8, 9 ,11,12,15, 35,36] and its generalizations.”
FRACTIONAL HEAT CONDUCTION EQUATION AND ASSOCIATED THERMAL STRESS (2004, background): “Other known particular cases correspond to the values β = 1/3 [ 62 ], and β = 2/3 [ 64 ], where Ai( x ) is the Airy function; the prime denotes the derivative.”
Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation (2009, background): “There are many works on the forward problem for fractional diffusion equations such as an initial value/ boundary value problem and we refer to Bazhlekova [2], Eidelman and Kochubei [6], Metzler and Klafter [27], Gorenflo, Luchko and Zabrejko [10], Hanyga [12], Luchko [19], [20] and the references t”