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