Analytical solutions for the multi-term time-space fractional reaction-diffusion equations on an infinite domain

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Xiao-Li Ding ◽  
Juan J. Nieto
Keyword(s):  
Analytical Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Infinite Domain ◽  
Time Space ◽  
Special Cases ◽  
Telegraph Equations ◽  
Wave Problems ◽  
Fractional Reaction

AbstractWe consider the analytical solutions of multi-term time-space fractional reaction-diffusion equations on an infinite domain. The results are presented in a compact and elegant form in terms of the Mittag-Leffler functions. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, fractional wave problems, and fractional telegraph equations scattered in the literature can be derived as special cases of the results presented in this paper.

scholarly journals Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

2011 ◽  
Vol 52 ◽  
pp. 395 ◽  
Author(s):  
Qianqian Yang ◽  
Tim Moroney ◽  
Kevin Burrage ◽  
Ian Turner ◽  
Fawang Liu
Keyword(s):  
Numerical Methods ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Time Space ◽  
Fractional Reaction

scholarly journals NEW EXACT SOLUTIONS OF SPATIALLY AND TEMPORALLY VARYING REACTION-DIFFUSION EQUATIONS

2008 ◽  
Vol 06 (04) ◽  
pp. 371-381 ◽  
Author(s):  
NALINI JOSHI ◽  
TEGAN MORRISON
Keyword(s):  
Reaction Diffusion ◽  
Elliptic Functions ◽  
Point Of View ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Source Terms ◽  
Symmetry Approach ◽  
New Exact Solutions ◽  
Special Cases ◽  
New Feature

This paper considers reaction-diffusion equations from a new point of view, by including spatiotemporal dependence in the source terms. We show for the first time that solutions are given in terms of the classical Painlevé transcendents. We consider reaction-diffusion equations with cubic and quadratic source terms. A new feature of our analysis is that the coefficient functions are also solutions of differential equations, including the Painlevé equations. Special cases arise with elliptic functions as solutions. Additional solutions given in terms of equations that are not integrable are also considered. Solutions are constructed using a Lie symmetry approach.

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