scholarly journals Semi-analytical solutions for cubic autocatalytic reaction-diffusion equations; the effect of a precursor chemical

2012 ◽  
Vol 53 ◽  
pp. 511
Author(s):  
Muteb R Alharthi ◽  
Tim Marchant ◽  
Mark Nelson
Keyword(s):  
Analytical Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Autocatalytic Reaction ◽  
Diffusion Equations

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.

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