Time-fractional telegraph equations and telegraph processes with brownian time

By Enzo Orsingher, Luisa Beghin. 2004

314 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/a59d8d83786e90c16432d6d6b8a1148fd6b5166c

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Citations in the corpus

Fractional diffusion equations and processes with randomly varying time. (2011, background): “λ2 − c2β2 and η2 =−λ− √ λ2 − c2β2 [see Orsingher and Beghin (2004), formula (2.”
Implicit difference approximation for the time fractional diffusion equation (2006, background): “Enzo et al. [ 3 ] and Luisa et al. [13] considered and proved the solutions to the Cauchy problem of the fractional telegraph equation can be expressed as the distribution of a suitable composition of dierent processes.”
Fractional Poisson processes and related planar random motions (2009, unknown): “…(2.18) and (2.19), we obtain the inverse Laplace transform as Gν(u, t) = 1 Γ(1− ν) ∫ +∞ 0 d y ∫ t 0 (t −w)−ν fν(w; y)eλy(u−1)dw. (2.20) It has been proved in Orsingher and Beghin (2004) that the solution v2ν to (2.12) can be expressed as v2ν(y, t) = 1 2Γ(1− ν) ∫ t 0 (t −w)−ν fν(w; |y |)dw, y…”
Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method (2016, methodology): “2) where 0 < α = 2β < 2, was obtained in [22] in terms of the inverse Fourier transform.”
On a fractional linear birth-death process (2011, unknown): “3) in [6] for c= 1, that being therefore ∫ ∞ 0 ePr{T2ν(t) ∈ ds}= e ν z ds.”
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density (2013, background): “In particular, we mention here the articles [4] and [31], where this problem was solved for the so called timefractional telegraph equation that corresponds to a very special choice of the weight function, namely for p(β) = δ(β − 2α)+ 2λδ(β −α), 0 < α ≤ 1.”