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Title: An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative
Authors: Kilbas, Anatoly
Repin, Oleg
Keywords: Partial Differential Equation of Mixed Type
Fractional Integrals and Derivatives
Gauss Hypergeometric Function
Mittag-Leffler Functions
Generalized Hypergeometric Series
Issue Date: 2010
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 13, No 1, (2010), 69p-84p
Abstract: The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel, the uniqueness and existence of a solution of the considered problem are proved, and its explicit solution is established in terms of the new special function.
Description: Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.
ISSN: 1311-0454
Appears in Collections:2010

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