This article is cited in 3 papers

Differential Equations and Mathematical Physics

Cauchy problem for a parabolic equation with Bessel operator and Riemann–Liouville partial derivative

F. G. Khushtova

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

Abstract: In this paper Cauchy problem for a parabolic equation with Bessel operator and with Riemann–Liouville partial derivative is considered. The representation of the solution is obtained in terms of integral transform with Wright function in the kernel. It is shown that when this equation becomes the fractional diffusion equation, obtained solution becomes the solution of Cauchy problem for the corresponding equation. The uniqueness of the solution in the class of functions that satisfy the analogue of Tikhonov condition is proved.

Keywords: fractional calculus, Riemann–Liouville integral-differential operator, differential equations with partial fractional derivatives, parabolic equation, Bessel operator, the modified Bessel function of the first kind, Wright function, the integral transform with Wright function in the kernel, Fox $H$-function, Cauchy problem, Tikhonov condition.

UDC: 517.968.7

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

Original article submitted 05/XI/2015
revision submitted – 07/II/2016

DOI: 10.14498/vsgtu1455

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