Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem

Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem

In the paper, a fundamental solution of the fractional dual-phase-lagging heat conduction problem is obtained. The considerations concern the 1D Cauchy problem in a whole-space domain. A solution of the initial-boundary problem is determined by using the Fourier–Laplace transform technique. The fina...

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Main Authors: Mariusz Ciesielski, Urszula Siedlecka
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Symmetry
Subjects:
heat conduction
dual-phase lag equation
Caputo fractional derivative
Cauchy problem
Fourier–Laplace transform
Online Access:https://www.mdpi.com/2073-8994/13/8/1333
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spelling doaj-77bf549f1b0d49aeb88fa65c4f3e91e62021-08-26T14:23:40ZengMDPI AGSymmetry2073-89942021-07-01131333133310.3390/sym13081333Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy ProblemMariusz Ciesielski0Urszula Siedlecka1Department of Computer Science, Czestochowa University of Technology, 42-201 Czestochowa, PolandDepartment of Mathematics, Czestochowa University of Technology, 42-201 Czestochowa, PolandIn the paper, a fundamental solution of the fractional dual-phase-lagging heat conduction problem is obtained. The considerations concern the 1D Cauchy problem in a whole-space domain. A solution of the initial-boundary problem is determined by using the Fourier–Laplace transform technique. The final form of solution is given in a form of a series. One of the properties of the derived fundamental solution of the considered problem with the initial condition expressed be the Dirac delta function is that it is symmetrical. The effect of the time-fractional order of the Caputo derivatives and the phase-lag parameters on the temperature distribution is investigated numerically by using the method which is based on the Fourier-series quadrature-type approximation to the Bromwich contour integral.https://www.mdpi.com/2073-8994/13/8/1333heat conductiondual-phase lag equationCaputo fractional derivativeCauchy problemFourier–Laplace transform
collection DOAJ
language English
format Article
sources DOAJ
author Mariusz Ciesielski
Urszula Siedlecka
spellingShingle Mariusz Ciesielski
Urszula Siedlecka
Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem
Symmetry
heat conduction
dual-phase lag equation
Caputo fractional derivative
Cauchy problem
Fourier–Laplace transform
author_facet Mariusz Ciesielski
Urszula Siedlecka
author_sort Mariusz Ciesielski
title Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem
title_short Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem
title_full Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem
title_fullStr Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem
title_full_unstemmed Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem
title_sort fractional dual-phase lag equation—fundamental solution of the cauchy problem
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2021-07-01
description In the paper, a fundamental solution of the fractional dual-phase-lagging heat conduction problem is obtained. The considerations concern the 1D Cauchy problem in a whole-space domain. A solution of the initial-boundary problem is determined by using the Fourier–Laplace transform technique. The final form of solution is given in a form of a series. One of the properties of the derived fundamental solution of the considered problem with the initial condition expressed be the Dirac delta function is that it is symmetrical. The effect of the time-fractional order of the Caputo derivatives and the phase-lag parameters on the temperature distribution is investigated numerically by using the method which is based on the Fourier-series quadrature-type approximation to the Bromwich contour integral.
topic heat conduction
dual-phase lag equation
Caputo fractional derivative
Cauchy problem
Fourier–Laplace transform
url https://www.mdpi.com/2073-8994/13/8/1333
work_keys_str_mv AT mariuszciesielski fractionaldualphaselagequationfundamentalsolutionofthecauchyproblem
AT urszulasiedlecka fractionaldualphaselagequationfundamentalsolutionofthecauchyproblem
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