Numerical treatment of fractional order Cauchy reaction diffusion equations

被引：21
作者：
Ali, Sajjad [1 ]
Bushnaq, Samia [1 ,2 ]
Shah, Kamal [1 ,3 ]
Arif, Muhammad [1 ]
机构：
[1] Abdul Wali Khan Univ, Dept Math, Mardan, Pakistan
[2] Princess Sumaya Univ Technol, Dept Sci, Amman 11941, Jordan
[3] Univ Malakand, Dept Math, Chakadara Dir L, Khyber Pakhtunk, Pakistan
来源：
CHAOS SOLITONS & FRACTALS | 2017年 / 103卷
关键词：
Optimal homotopy asymptotic method; Fractional order Cauchy reaction diffusion equations; Analytical and approximate solution; HOMOTOPY ASYMPTOTIC METHOD;
D O I：
10.1016/j.chaos.2017.07.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this manuscript, an approximate method for the numerical solutions of fractional order Cauchy reaction diffusion equations is considered. The concerned method is known as optimal homotopy asymptotic method (OHAM). With the help of the mentioned method, we handle approximate solutions to the aforesaid equation. Some test problems are provided at which the adapted technique has been applied. The comparison between absolute and exact solution are also provided which reveals that the adapted method is highly accurate. For tabulation and plotting, we use matlab software. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：578 / 587
页数：10
相关论文
共 25 条
  • [1] On right fractional calculus
    Anastassiou, George A.
    [J]. CHAOS SOLITONS & FRACTALS, 2009, 42 (01) : 365 - 376
  • [2] [Anonymous], 2000, Applications of Fractional Calculus in Physics
  • [3] [Anonymous], 2015, J APPL ENV BIOL SCI
  • [4] On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation
    Atangana, Abdon
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2016, 273 : 948 - 956
  • [5] Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular
    Fabian Morales-Delgado, Victor
    Francisco Gomez-Aguilar, Jose
    Yepez-Martinez, Huitzilin
    Baleanu, Dumitru
    Fabricio Escobar-Jimenez, Ricardo
    Hugo Olivares-Peregrino, Victor
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2016,
  • [6] Fractional Lienard type model of a pipeline within the fractional derivative without singular kernel
    Gomez-Aguilar, J. F.
    Torres, L.
    Yepez-Martinez, H.
    Baleanu, D.
    Reyes, J. M.
    Sosa, I. O.
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2016,
  • [7] Modeling diffusive transport with a fractional derivative without singular kernel
    Gomez-Aguilar, J. F.
    Lopez-Lopez, M. G.
    Alvarado-Martinez, V. M.
    Reyes-Reyes, J.
    Adam-Medina, M.
    [J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2016, 447 : 467 - 481
  • [8] 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.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 30 (1-3) : 115 - 127
  • [9] Application of homotopy perturbation method to nonlinear wave equations
    He, JH
    [J]. CHAOS SOLITONS & FRACTALS, 2005, 26 (03) : 695 - 700
  • [10] Homotopy perturbation technique
    He, JH
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1999, 178 (3-4) : 257 - 262
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