Mixed problem for nonlinear integro-differential equation involvingcube of parabolic operator

In this paper we consider problems of one-valued solubility of mixed problem for a nonlinear integro-differential
equation, consisting cube of parabolic operator. By the Fourier nonlinear method of separation variables we obtain
the countable system of nonlinear integral equation.

cube of parabolic operator, argument deviation, countable system of nonlinear integral equations, general derivatives, convergence of series