000			02515cam a2200349 a 4500
003			EG-GiCUC
005			20250223032057.0
008			181010s2018 ua dh f m 000 0 eng d
040			_aEG-GiCUC _beng _cEG-GiCUC
041	0		_aeng
049			_aDeposite
097			_aPh.D
099			_aCai01.12.17.Ph.D.2018.Ka.S
100	0		_aKarima Mohamed Oraby Mohamed
245	1	0	_aSemi-groups of operators on time scales and dynamic equations / _cKarima Mohamed Oraby Mohamed ; Supervised A. E. Hamza , Mohamed S. Metwally, M. H. Aburisha
246	1	5	_aأنصاف زمر المؤثرات علي مقاييس الزمن و المعادلات الديناميكية
260			_aCairo : _bKarima Mohamed Oraby Mohamed , _c2018
300			_a124 P. : _bcharts , facsimiles ; _c25cm
502			_aThesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics
520			_aIn 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{u2206}(t) = Ax(t) + Bu(t), t {u2208} T, x(x) = xx {u2208} D(A), and control Volterra integro-dynamic equations of the form x{u2206}(t) = Ax(t) + Z t 0 G(t, s)x(s){u2206}s + Bu(t), t {u2208} T, x(x) = xx {u2208} 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 {u2208} 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 {u2192} U. Finally, we investigate many types of stability of abstract dynamic equations of the form x{u2206}(t) = F(t, x), x(x) = xx {u2208} X, t {u2208} Tx+ := [x, {u221E})T, where F : T{u00D7}X {u2192} X is rd-continuous in the {uFB01}rst argument with F(t,0) = 0, by using the Lyapunov{u2019}s second method. We construct a Lyapunov function to obtain new su{uFB03}cient conditions for stability of some of abstract dynamic equations on time scales.
530			_aIssued also as CD
653		4	_aDynamic equations
653		4	_aLyapunov stability theory
653		4	_aTime scales
700	0		_aAlaa Eldeen Hamza , _eSupervisor
700	0		_aMohamed S. Metwally , _eSupervisor
700	0		_aMomen H. Aburisha , _eSupervisor
856			_uhttp://172.23.153.220/th.pdf
905			_aNazla _eRevisor
905			_aShimaa _eCataloger
942			_2ddc _cTH
999			_c67883 _d67883