Analytical solution of the space-time fractional hyperdiffusion equation

被引：6
|
作者：
Tawfik, Ashraf M. [1 ,2 ]
Fichtner, Horst [1 ]
Elhanbaly, A. [2 ]
Schlickeiser, Reinhard [1 ]
机构：
[1] Ruhr Univ Bochum, Inst Theoret Phys 4, Univ Str 150, D-44780 Bochum, Germany
[2] Mansoura Univ, Theoret Phys Res Grp, Mansoura 35516, Egypt
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2018年 / 510卷
关键词：
Fractional calculus; Anomalous diffusion; Energetic particles; DIFFUSION-ADVECTION EQUATION; SUPERDIFFUSIVE TRANSPORT; MODELS;
D O I：
10.1016/j.physa.2018.07.002
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The so-called fractional hyperdiffusion equation is presented to develop a fractional derivative model of the transport of energetic particles. The fractional hyperdiffusion equation is defined in terms of Caputo and Riesz fractional derivatives for time and space, respectively. The solution is obtained by using the Laplace-Fourier transforms and given in terms of the M-Wright and Fox's H functions. Profiles of particle densities are illustrated for different values of space-fractional order. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：178 / 187
页数：10
相关论文
共 50 条
  • [1] ANALYTICAL SOLUTION OF THE SPACE-TIME FRACTIONAL NONLINEAR SCHRODINGER EQUATION
    Abdel-Salam, Emad A-B.
    Yousif, Eltayeb A.
    El-Aasser, Mostafa A.
    REPORTS ON MATHEMATICAL PHYSICS, 2016, 77 (01) : 19 - 34
  • [2] Analytical solution for a generalized space-time fractional telegraph equation
    Fino, Ahmad Z.
    Ibrahim, Hassan
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (14) : 1813 - 1824
  • [3] Analytical Solution of Generalized Space-Time Fractional Cable Equation
    Saxena, Ram K.
    Tomovski, Zivorad
    Sandev, Trifce
    MATHEMATICS, 2015, 3 (02) : 153 - 170
  • [4] Solution for a Space-time Fractional Diffusion Equation
    Liu, Qiyu
    Lv, Longjin
    PROCEEDINGS OF THE 2017 2ND INTERNATIONAL CONFERENCE ON MODELLING, SIMULATION AND APPLIED MATHEMATICS (MSAM2017), 2017, 132 : 180 - 184
  • [5] Analytical Solution of the Space-Time Fractional Reaction–Diffusion Equation with Variable Coefficients
    E. I. Mahmoud
    Journal of Mathematical Sciences, 2024, 285 (4) : 505 - 519
  • [6] Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation
    Khaled A. Gepreel
    Mohamed S. Mohameda
    ChinesePhysicsB, 2013, 22 (01) : 33 - 38
  • [7] Approximate analytical solution of two-dimensional space-time fractional diffusion equation
    Pandey, Prashant
    Kumar, Sachin
    Gomez, Francisco
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (12) : 7194 - 7207
  • [8] Analytical Approximate Solution of Space-Time Fractional Diffusion Equation with a Moving Boundary Condition
    Das, Subir
    Kumar, Rajnesh
    Gupta, Praveen Kumar
    ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2011, 66 (05): : 281 - 288
  • [9] Analytical solution of the generalized space-time fractional ultra-hyperbolic differential equation
    Dorrego, Gustavo A.
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2022, 33 (04) : 264 - 275
  • [10] Analytical approximate solution for nonlinear space-time fractional Klein-Gordon equation
    Gepreel, Khaled A.
    Mohamed, Mohamed S.
    CHINESE PHYSICS B, 2013, 22 (01)
12345