Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact

被引：18

作者：

Datsko, Bohdan ^{[1
,2
]}

Podlubny, Igor ^{[3
]}

Povstenko, Yuriy ^{[4
]}

机构：

[1] Rzeszow Univ Technol, Fac Math & Appl Phys, Powstancow Warszawy 8, PL-35959 Rzeszow, Poland

[2] NAS Ukraine, Inst Appl Problems Mech & Math, UA-79060 Lvov, Ukraine

[3] Tech Univ Kosice, BERG Fac, B Nemcovej 3, Kosice 04200, Slovakia

[4] Jan Dlugosz Univ Czestochowa, Fac Math & Nat Sci, Armii Krajowej 13-15, PL-42200 Czestochowa, Poland

来源：

MATHEMATICS | 2019年 / 7卷 / 05期

关键词：

fractional calculus; mass absorption; diffusion-wave equation; Caputo derivative; harmonic impact; Laplace transform; Fourier transform; Mittag-Leffler function; BIOHEAT EQUATION; HEAT-CONDUCTION;

D O I：

10.3390/math7050433

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The time-fractional diffusion equation with mass absorption in a sphere is considered under harmonic impact on the surface of a sphere. The Caputo time-fractional derivative is used. The Laplace transform with respect to time and the finite sin-Fourier transform with respect to the spatial coordinate are employed. A graphical representation of the obtained analytical solution for different sets of the parameters including the order of fractional derivative is given.

引用

页数：11

共 50 条

[31] Analysis of a meshless generalized finite difference method for the time-fractional diffusion-wave equation
Qing, Lanyu
Li, Xiaolin
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 172 : 134 - 151
[32] Non-axisymmetric solutions to time-fractional diffusion-wave equation in an infinite cylinder
Yuriy Povstenko
Fractional Calculus and Applied Analysis, 2011, 14 : 418 - 435
[33] Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density
Gorenflo, Rudolf
Luchko, Yuri
Stojanovic, Mirjana
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2013, 16 (02) : 297 - 316
[34] Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density
Rudolf Gorenflo
Yuri Luchko
Mirjana Stojanović
Fractional Calculus and Applied Analysis, 2013, 16 : 297 - 316
[35] NON-AXISYMMETRIC SOLUTIONS TO TIME-FRACTIONAL DIFFUSION-WAVE EQUATION IN AN INFINITE CYLINDER
Povstenko, Yuriy
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2011, 14 (03) : 418 - 435
[36] Conservation laws for time-fractional subdiffusion and diffusion-wave equations
Lukashchuk, Stanislav Yu
NONLINEAR DYNAMICS, 2015, 80 (1-2) : 791 - 802
[37] Conservation laws for time-fractional subdiffusion and diffusion-wave equations
Stanislav Yu. Lukashchuk
Nonlinear Dynamics, 2015, 80 : 791 - 802
[38] Subordination in a Class of Generalized Time-Fractional Diffusion-Wave Equations
Bazhlekova Emilia
Fractional Calculus and Applied Analysis, 2018, 21 : 869 - 900
[39] SUBORDINATION IN A CLASS OF GENERALIZED TIME-FRACTIONAL DIFFUSION-WAVE EQUATIONS
Bazhlekova, Emilia
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (04) : 869 - 900
[40] Numerical simulation for time-fractional diffusion-wave equations with time delay
Yaoyao Zhang
Zhibo Wang
Journal of Applied Mathematics and Computing, 2023, 69 : 137 - 157

← 1 2 3 4 5 →