A Nonlocal Boundary Value Problem with the Frankl Condition for an Equation of Mixed Parabolic-Hyperbolic Type with the Fractional Gerasimov–Caputo Operator

A new nonlocal boundary value problem with the Frankl condition for an equation of mixed parabolic-hyperbolic type with a fractional-order operator in the sense of Gerasimov-Caputo is formulated. The line of change of type is not a characteristic of the equation. The proposed new nonlocal condition connects the points on the boundaries of the parabolic part and the hyperbolic part of the domain. This problem is a generalization of well-known Frankl-type problems. The unique solvability of this problem is proved in the sense of the classical and strong solutions.

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