Kilbas, Anatoly A.; Repin, Oleg A. An analog of the Tricomi problem for a mixed type equation with a partial fractional derivative. (English) Zbl 1201.35148 Fract. Calc. Appl. Anal. 13, No. 1, 69-84 (2010). 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. Reviewer: Elena Gavrilova (Sofia) Cited in 22 Documents MSC: 35M10 PDEs of mixed type 35R11 Fractional partial differential equations 26A33 Fractional derivatives and integrals 33C05 Classical hypergeometric functions, \({}_2F_1\) 33E12 Mittag-Leffler functions and generalizations 33C20 Generalized hypergeometric series, \({}_pF_q\) Keywords:partial differential equation of mixed type; fractional integrals and derivatives; Gauss hypergeometric function; Mittag-Leffler functions; generalized hypergeometric series PDFBibTeX XMLCite \textit{A. A. Kilbas} and \textit{O. A. Repin}, Fract. Calc. Appl. Anal. 13, No. 1, 69--84 (2010; Zbl 1201.35148) Full Text: EuDML