This article is cited in 6 papers

Differential Equations and Mathematical Physics

Fundamental solution of the model equation of anomalous diffusion of fractional order

F. G. Khushtova

Institution of Applied Mathematics and Automation, Nal'chik, 360000, Russian Federation

Abstract: 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.

Keywords: anomalous diffusion, diffusion fractional order, Riemann–Liouville operator, fundamental solution, general representation of solution, modified Bessel function, Wright function, integral transformation wich Wright function in kernel.

UDC: 517.968.7

MSC: 35A08, 35A22, 35R11, 35C15

Original article submitted 15/VIII/2015
revision submitted – 19/X/2015

DOI: 10.14498/vsgtu1445

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