Partial Differential Equation of Mixed Type Fractional Integrals and Derivatives Gauss Hypergeometric Function Mittag-Leffler Functions Generalized Hypergeometric Series
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 13, No 1, (2010), 69p-84p
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.