Geodesic
Fundamental solution of the model equation of anomalous diffusion of fractional order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 4, pp. 722-735

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Fundamental solution of the model equation of anomalous diffusion with Riemann–Liouville operator is constructed. Using the properties of the integral transformation with Wright function in kernel, we give estimates for the fundamental solution. When the considered equation transformes into the diffusion equation of fractional order, constructed fundamental solution goes into the corresponding fundamental solution of the diffusion equation of fractional order. General solution of the model equation of anomalous diffusion of fractional order is constructed.
Mots-clés : anomalous diffusion, diffusion fractional order
Keywords: Riemann–Liouville operator, fundamental solution, general representation of solution, modified Bessel function, Wright function, integral transformation wich Wright function in kernel. 
@article{VSGTU_2015_19_4_a10,
     author = {F. G. Khushtova},
     title = {Fundamental solution of the model equation of anomalous diffusion of fractional order},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {722--735},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2015_19_4_a10/}
}
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F. G. Khushtova. Fundamental solution of the model equation of anomalous diffusion of fractional order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 4, pp. 722-735. http://geodesic.mathdoc.fr/item/VSGTU_2015_19_4_a10/