Authors: Želi, Velibor
Zorica, Dušan 
Title: Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law
Journal: Physica A: Statistical Mechanics and its Applications
Volume: 492
First page: 2316
Last page: 2335
Issue Date: 15-Feb-2018
Rank: M21
ISSN: 0378-4371
DOI: 10.1016/j.physa.2017.11.150
Abstract: 
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams–Bashforth and Grünwald–Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.
Keywords: Cattaneo type heat conduction law | Finite differences | Fractional distributed-order constitutive equation | Integral transforms
Publisher: Elsevier
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Provincial Government of Vojvodina, Grant 114-451-2098

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