Existence of Solution of Space-Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space

被引：0

作者：

Zhang, Kangqun ^{[1
]}

机构：

[1] Nanjing Inst Technol, Dept Math & Phys, Nanjing 211167, Peoples R China

来源：

ADVANCES IN MATHEMATICAL PHYSICS | 2020年 / 2020卷

关键词：

TRANSFORM;

D O I：

10.1155/2020/1545043

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we consider Cauchy problem of space-time fractional diffusion-wave equation. Applying Laplace transform and Fourier transform, we establish the existence of solution in terms of Mittag-Leffler function and prove its uniqueness in weighted Sobolev space by use of Mikhlin multiplier theorem. The estimate of solution also shows the connections between the loss of regularity and the order of fractional derivatives in space or in time.

引用

页数：6

共 50 条

[31] Simultaneous inversion for the exponents of the fractional time and space derivatives in the space-time fractional diffusion equation
Tatar, SalIh
Tinaztepe, Ramazan
Ulusoy, Suleyman
APPLICABLE ANALYSIS, 2016, 95 (01) : 1 - 23
[32] Solvability Cauchy Problem for Time-Space Fractional Diffusion-Wave Equation with Variable Coefficient
H. H. Turdiev
Lobachevskii Journal of Mathematics, 2024, 45 (10) : 5281 - 5294
[33] Solutions of the space-time fractional Cattaneo diffusion equation
Qi, Haitao
Jiang, Xiaoyun
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2011, 390 (11) : 1876 - 1883
[34] The space-time fractional diffusion equation with Caputo derivatives
Huang F.
Liu F.
Journal of Applied Mathematics and Computing, 2005, 19 (1-2) : 179 - 190
[35] Modeling and simulation of the fractional space-time diffusion equation
Gomez-Aguilar, J. F.
Miranda-Hernandez, M.
Lopez-Lopez, M. G.
Alvarado-Martinez, V. M.
Baleanu, D.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 30 (1-3) : 115 - 127
[36] The Space-Time Spectral Method for a Fractional Diffusion Equation
Huang, Yu
PROCEEDINGS OF THE 2010 INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS AND PHYSICS, VOL 2: ADVANCES ON APPLIED MATHEMATICS AND COMPUTATION MATHEMATICS, 2010, : 347 - 350
[37] Fourth-order numerical method for the space time tempered fractional diffusion-wave equation
Dehghan, Mehdi
Abbaszadeh, Mostafa
Deng, Weihua
APPLIED MATHEMATICS LETTERS, 2017, 73 : 120 - 127
[38] A SPACE-TIME SPECTRAL METHOD FOR THE TIME FRACTIONAL DIFFUSION EQUATION
Li, Xianjuan
Xu, Chuanju
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (03) : 2108 - 2131
[39] An Efficient Space-Time Method for Time Fractional Diffusion Equation
Shen, Jie
Sheng, Chang-Tao
JOURNAL OF SCIENTIFIC COMPUTING, 2019, 81 (02) : 1088 - 1110
[40] Space-Time Estimates on Damped Fractional Wave Equation
Chen, Jiecheng
Fan, Dashan
Zhang, Chunjie
ABSTRACT AND APPLIED ANALYSIS, 2014,

← 1 2 3 4 5 →