On a nonlocal boundary value problem for a degenerate parabolic-hyperbolic equation with fractional derivative. (English) Zbl 1490.35232

Ochilova, N. K.; Yuldashev, T. K.

Lobachevskii J. Math. 43, No. 1, 229-236 (2022).

Summary: The goal of this work is to study the existence and uniqueness of the solution to a nonlocal boundary value problem for a degenerate differential equation of mixed type. A parabolic-hyperbolic equation with a fractional Gerasimov-Caputo derivative is considered. The uniqueness of the solution is proved by the integral energy method using the some properties of hypergeometric functions and integro-differential operators of fractional order. The existence of the solution is proved by the method of integral equations.

MSC:

35M10	PDEs of mixed type
35R11	Fractional partial differential equations

Keywords:

Gaussian hypergeometric function; Cauchy problem; existence and uniqueness; method of integral equations; fractional Gerasimov-Caputo derivative

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