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

Kilbas, 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 -