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In this paper, we analyze some initial-boundary value problems forthe subdiffusion equation with a fractional dynamic boundary condition in aone-dimensional bounded domain. First, we establish the unique solvabilityin the Hölder space of the initial-boundary value problems for the equation , , where L is a uniformly ellipticoperator with smooth coefficients with the fractional dynamic boundary condition. Second, we apply the contraction theorem to prove the existence anduniqueness locally in time in the Hölder classes of the solution to the corresponding nonlinear problems

Existence and Uniqueness of the Solutions for Some Initial-Boundary Value Problems with the Fractional Dynamic Boundary Condition