Existence and uniqueness of solutions for loaded mixed-type equation with fractional integral operators

This paper investigates a boundary value problem for a secondorder integro-differential equation of mixed parabolic-hyperbolic type with variable coefficients and fractional loading. The main focus is on establishing the existence and uniqueness of a regular solution under integral gluing conditions imposed on the line of type change. The method of integral equations is employed to study the solvability of the problem. Sufficient conditions for unique solvability are formulated and proven. The results contribute to the theory of mixed-type equations with nonlocal and fractional conditions, which are relevant in various physical models involving memory and hereditary effects.

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