Solution of fractional bioheat equation in terms of Fox’s H-function

Abstract

Present paper deals with the solution of time and space fractional Pennes bioheat equation. We consider time fractional derivative and space fractional derivative in the form of Caputo fractional derivative of order and Riesz–Feller fractional derivative of order respectively. We obtain solution in terms of Fox’s H-function with some special cases, by using Fourier–Laplace transforms.

Fractional heat conduction with heat absorption in a sphere under Dirichlet boundary condition

“…B Yuriy Povstenko j.povstenko@ajd.czest.pl Joanna Klekot joanna.klekot@im.pcz.pl 1 was considered, e.g., in Carslaw and Jaeger (1959), Crank (1975), Nyborg (1988), Polyanin (2002). Here, T is temperature, t is time, a stands for the thermal diffusivity coefficient, denotes the Laplace operator, the coefficient b describes the heat absorption (heat release).…”

“…(2) in the case of one Cartesian spatial coordinate (Damor et al 2016;Ferrás et al 2015;Qin and Wu 2016;Vitali et al 2017). Here, we study Eq.…”

Bio-Heat Models Revisited: Concepts, Derivations, Nondimensalization and Fractionalization Approaches

“…The model of Damor et al [125] is a fractional version of the bio-heat equation by a simple replacement the time derivative with a fractional counterpart as Caputo derivative (order α ∈ (0, 1]) with singular (power-law) kernel and the spatial derivative by a Riesz-Feller fractional derivative of order β ∈ (0, 2], namely…”

“…Otherwise, for α = 1 and a Riemann-Liouville space derivative of order γ ∈ (0, 2] [see (141)] the formal fractionalization results in [126] (141) For β = 2 the model (138) reduces to [125]…”

A coupling method involving the Sumudu transform and the variational iteration method for a class of local fractional diffusion equations

“…We begin with the following local fractional diffusion equation in fractal one-dimensional space (see [3,5,18])…”