An analog of the Tricomi problem for a mixed type equation with a partial fractional derivative.

*(English)*Zbl 1201.35148An 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.

Reviewer: Elena Gavrilova (Sofia)

##### MSC:

35M10 | PDE of mixed type |

35R11 | Fractional partial differential equations |

26A33 | Fractional derivatives and integrals (real functions) |

33C05 | Classical hypergeometric functions, ${}_{2}{F}_{1}$ |

33E12 | Mittag-Leffler functions and generalizations |

33C20 | Generalized hypergeometric series, ${}_{p}{F}_{q}$ |