The concentration of this paper on studying the functional properties and the solvability of Boundary-Value Linear Composed time-varying Descriptor operator system defined on suitable reflexive Hilbert space, using (Variational) approach, which is based on constructing a appropriate functional form whose the critical-points are the solution of the proposed operator system and vice versa. The validity of this (Variational) approach is depends on the positivity and symmetry of the Boundary-Value Linear Composed time-varying Descriptor operator system on Hilbert space using Composed Cartesian product bilinear. The needful mathematical requirements are extracted and proved. Arithmetic Algorithms are proposed. Some illustration and computations between the exact solution and the suggested formula are also involved.

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