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An analog of the Tricomi problem for a mixed type equation with a partial fractional derivative. (English) Zbl 1201.35148

An analog of Tricomi boundary value problem is for a special partial differential equation of mixed type is under consideration. It involves a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines.

Uniqueness and existence of a solution of the considered problem are proved by using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel. Its explicit solution is established in terms of the new special function.

MSC:
35M10PDE of mixed type
35R11Fractional partial differential equations
26A33Fractional derivatives and integrals (real functions)
33C05Classical hypergeometric functions, 2 F 1
33E12Mittag-Leffler functions and generalizations
33C20Generalized hypergeometric series, p F q