CS Department;
College of Computers and IT;
Taif University;
Taif;
KSA;
Department of Mathematics;
Faculty of Science;
Fayoum University;
Fayoum;
Egypt;
Mathematics Department;
Faculty of Science;
Taif University;
Taif;
KSA;
Constrained; Optimal; Control; Problems; Necessary; Optimality; Conditions; Parabolic; System; Adjoint; Problem; Exterior; Penalty; Function; Method; Existence; and; Uniqueness; Theorems;