# An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Fractional Calculus and Applied Analysis (2010)

- Volume: 13, Issue: 1, page 69-84
- ISSN: 1311-0454

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topKilbas, Anatoly, and Repin, Oleg. "An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative." Fractional Calculus and Applied Analysis 13.1 (2010): 69-84. <http://eudml.org/doc/219592>.

@article{Kilbas2010,

abstract = {Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.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.},

author = {Kilbas, Anatoly, Repin, Oleg},

journal = {Fractional Calculus and Applied Analysis},

keywords = {Partial Differential Equation of Mixed Type; Fractional Integrals and Derivatives; Gauss Hypergeometric Function; Mittag-Leffler Functions; Generalized Hypergeometric Series; partial differential equation of mixed type; fractional integrals and derivatives; Gauss hypergeometric function; Mittag-Leffler functions; generalized hypergeometric series},

language = {eng},

number = {1},

pages = {69-84},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative},

url = {http://eudml.org/doc/219592},

volume = {13},

year = {2010},

}

TY - JOUR

AU - Kilbas, Anatoly

AU - Repin, Oleg

TI - An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

JO - Fractional Calculus and Applied Analysis

PY - 2010

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 13

IS - 1

SP - 69

EP - 84

AB - Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.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.

LA - eng

KW - Partial Differential Equation of Mixed Type; Fractional Integrals and Derivatives; Gauss Hypergeometric Function; Mittag-Leffler Functions; Generalized Hypergeometric Series; partial differential equation of mixed type; fractional integrals and derivatives; Gauss hypergeometric function; Mittag-Leffler functions; generalized hypergeometric series

UR - http://eudml.org/doc/219592

ER -

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