Abstarct: In this thesis‎, ‎the eigenvalue assignment methods on the basis of similarity transformation‎, ‎matrix inverse eigenvalue problem‎, ‎and the method of partial eigenvalue assignment by the use of eigenvectors are applied to investigate and to find the solution of discrete-time and continuous-time descxriptor and discrete-time descxriptor fractional systems‎. ‎The first case is focused in two-dimensional fractional Roesser systems‎. ‎For stabilization of descxriptor fractional systems‎, ‎these systems are first converted to systems with unlimited increasing delays and controllability of this form is not applicable‎. ‎By limiting delays because the coefficient of delays are descending and using new definition of matrices will arrive standard systems but with bigger scale‎. ‎The eigenvalue assignment methods via similarity transformation and matrix inverse eigenvalue problem is applied in discrete-time systems by obtaining forward state and output feedback matrix and forward and propositional state and output feedback matrix and in continuous-time systems by obtaining derivative state and output feedback matrix and derivative and propositional state and output feedback matrix‎. ‎And the closed-loop matrix with desired eigenvalues is calculated‎. ‎The eigenvalue assignment using similarity transformation‎, ‎closed-loop matrix is calculated by the use of state feedback matrix‎. ‎Otherwise‎, ‎the eigenvalue assignment using similarity transformation‎, ‎output feedback matrix is obtained by calculated closed-loop matrix‎. ‎The second one is more applicable when output of system is more important‎. ‎Eigenvalue assignment is done with two aims‎. ‎First‎, ‎stabilization of unstable systems‎. ‎Second‎, ‎desired eigenvalue assigning‎. ‎In partial eigenvalue assignment‎, ‎just assigning of undesired eigenvalue of standard systems is needed while other ones‎, ‎desired eigenvalues‎, ‎are invariant‎. ‎Therefore‎, ‎smaller scale of systems will be concerned‎. ‎Partial eigenvalue assignment by eigenvectors has some superiorities rather than using orthogonality relations‎. ‎Further manners like drazin inverse‎, ‎shuffle algorithm‎, ‎‎Weierstrass decomposition‎, ‎and Kaczorek form are introduced and compared with eigenvalue assignment methods‎.