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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.

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