Karima Mohamed Oraby Mohamed <br/><br/>
Semi-groups of operators on time scales and dynamic equations /  
 أنصاف زمر المؤثرات علي مقاييس الزمن و المعادلات الديناميكية 
Karima Mohamed Oraby Mohamed ; Supervised A. E. Hamza , Mohamed S. Metwally, M. H. Aburisha 
 - Cairo :   Karima Mohamed Oraby Mohamed ,   2018 
 - 124 P. :   charts , facsimiles ;   25cm 
<br/><br/>Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics 
<br/><br/> In this thesis, we continue the development of the theory of C0-semigroups of bounded linear operators from a Banach space X into itself on a semigroup time scale T. Also, we study the stabilizability of control dynamic equations of the form x(t) = Ax(t) + Bu(t), t  T, x(x) = xx  D(A), and control Volterra integro-dynamic equations of the form x(t) = Ax(t) +  Z t 0  G(t, s)x(s)s + Bu(t), t  T, x(x) = xx  D(A), where G(t,s) is continuous in the variable t and rd-continuous in the variable s, A is the generator of a C0-semigroup and B  L(U, D(A)), the space of all bounded linear operators from a Banach space U ( the control space ) to the domain D(A) of A, by the feedback control u : T  U. Finally, we investigate many types of stability of abstract dynamic equations of the form x(t) = F(t, x), x(x) = xx  X, t  Tx+ := [x, )T, where F : TX  X is rd-continuous in the rst argument with F(t,0) = 0, by using the Lyapunovs second method. We construct a Lyapunov function to obtain new sucient conditions for stability of some of abstract dynamic equations on time scales. 
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<br/><br/><label>Subjects--Index Terms: </label>Dynamic equations  Lyapunov stability theory  Time scales