Geodesic
An approximate group classification of a perturbed subdiffusion equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 4, pp. 603-619

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A problem of the Lie point approximate symmetry group classification of a perturbed subdiffusion equation with a small parameter is solved. The classification is performed with respect to anomalous diffusion coefficient which is considered as a function of an independent variable. The perturbed subdiffusion equation is derived from a fractional subdiffusion equation with the Riemann-Liouville time-fractional derivative under an assumption that the order of fractional differentiation is close to unity. As it is follow from the classification results, the perturbed subdiffusion equation admits a more general Lie point symmetry group than the initial fractional subdiffusion equation. The obtained results permit to construct approximate invariant solutions for the perturbed subdiffusion equation corresponding to different functions of the anomalous diffusion coefficient. These solutions will also be the approximate solutions of the initial fractional subdiffusion equation.
Keywords: fractional differential equation, small parameter, approximate transformation group
Mots-clés : subdiffusion, group classification. 
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     author = {S. Yu. Lukashchuk},
     title = {An approximate group classification of a perturbed subdiffusion equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {603--619},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2016_20_4_a2/}
}
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S. Yu. Lukashchuk. An approximate group classification of a perturbed subdiffusion equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 4, pp. 603-619. http://geodesic.mathdoc.fr/item/VSGTU_2016_20_4_a2/