000			02729cam a2200337 a 4500
003			EG-GiCUC
005			20250223031855.0
008			171211s2016 ua d f m 000 0 eng d
040			_aEG-GiCUC _beng _cEG-GiCUC
041	0		_aeng
049			_aDeposite
097			_aM.Sc
099			_aCai01.12.17.M.Sc.2016.Mo.T
100	0		_aMohammed Hussein Hasan Alashwal
245	1	0	_aTheory of power quantum difference equations / _cMohammed Hussein Hasan Alashwal ; Supervised Alaa E. Hamza , Samir A. Ashour
246	1	5	_aنظرية المعادلات الفروقية للقوى الكمية
260			_aCairo : _bMohammed Hussein Hasan Alashwal , _c2016
300			_a85 P. : _bcharts ; _c25cm
502			_aThesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics
520			_a This thesis introduces the theory of linear power quantum difference equations associated with the power quantum difference operator. We define the power quantum exponential and trigonometric (hyperbolic) functions and give some of their properties. We prove that they are solutions of difference equations of first and second order respectively. Next, we apply the method of successive approximations to obtain the existence and uniqueness of solutions of linear difference equations in Banach spaces in both local and global cases. Then, we study the theory of linear power quantum difference equations. We introduce the power quantum Wronskian and prove its properties. We show that it is an effective tool to determine whether set of solutions is a fundamental set or not. Hence, we obtain Liouville{u2019}s formula for power quantum difference equations. Also, we derive the solution of the first order linear power quantum difference equation with non-constant coefficients. We derive solutions of Euler-Cauchy difference equations as special cases of second order linear difference equations. Thereafter, we are concerned with constructing a fundamental set of solutions of homogeneous power quantum linear difference equations when the coefficients are constant. Finally, we establish many Pachpatte{u2019}s inequalities based on the power quantum difference operator and as special cases we obtain Gronwall{u2019}s and Bernoulli{u2019}s inequalities associated with this operator
530			_aIssued also as CD
653		4	_aExistence and uniqueness of solutions
653		4	_aPower quantum difference operator
653		4	_aTheory of power quantum difference equations
700	0		_aAlaa E. Hamza , _eSupervisor
700	0		_aSamir A. Ashour , _eSupervisor
856			_uhttp://172.23.153.220/th.pdf
905			_aNazla _eRevisor
905			_aShimaa _eCataloger
942			_2ddc _cTH
999			_c63962 _d63962