Geodesic
An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative
Fractional calculus and applied analysis, Tome 13 (2010) no. 1, pp. 69-84

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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.
Keywords: Partial Differential Equation of Mixed Type, Fractional Integrals and Derivatives, Gauss Hypergeometric Function, Mittag-Leffler Functions, Generalized Hypergeometric Series 
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     author = {Kilbas, Anatoly and Repin, Oleg},
     title = {An {Analog} of the {Tricomi} {Problem} for a {Mixed} {Type} {Equation} with a {Partial} {Fractional} {Derivative}},
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Kilbas, Anatoly; Repin, Oleg. An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative. Fractional calculus and applied analysis, Tome 13 (2010) no. 1, pp. 69-84. http://geodesic.mathdoc.fr/item/FCAA_2010_13_1_a5/