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The Tra.eling Wa.e Solutions for Some Nonlinea. PDEs in Ma.hema.ica. Physics

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a.plied Ma.hema.ics 2011年第3期2卷 343-347页

作者： khaled a. gepreel Sa.eh Omra. Sa.ed K. Ela.a. 不详

In the present a.ticle, we construct the exa.t tra.eling wa.e solutions of some nonlinea. PDEs in the ma.hema.ica. physics via.(1 + 1) dimensiona. Ka.p Kupershmit equa.ion, the (1 + 1) dimensiona. seventh order KdV equa.ion a.d (1 + 1) dimensiona. Kersten-Kra.il Shchik equa.ions by using the modified trunca.ed expa.sion method. New exa.t solutions of these equa.ions a.e found.

关键词： Conjuga.e Modified Trunca.ed Expa.sion Method Tra.eling Wa.e Solutions Nonlinea. Evolution Equa.ions

Exa.t solutions for nonlinea. pa.tia. fra.tiona. differentia. equa.ions

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Chinese Physics B 2012年第11期21卷 32-38页

作者： khaled a.gepreel Sa.eh Omra. Ma.hema.ics Depa.tment Faculty of ScienceZagazig University Ma.hema.ics Depa.tment Faculty of ScienceTaif University Ma.hema.ics Depa.tment Faculty of scienceSouth Valley University

′In this a.ticle, we use the fra.tiona. complex tra.sforma.ion to convert nonlinea. pa.tia. fra.tiona. differentia. equa.ions to nonlinea. ordina.y differentia. equa.ions. We use the improved （G′/G）-expa.sion function method to ca.cula.e the exa.t solutions to the time- a.d spa.e-fra.tiona. deriva.ive foa. dra.na.e equa.ion a.d the time- a.d spa.e-fra.tiona. deriva.ive nonlinea. KdV equa.ion. This method is efficient a.d powerful for solving wide cla.ses of nonlinea. evolution fra.tiona. order equa.ions.

关键词： fra.tiona. ca.culus complex tra.sforma.ion modified Riema.n-Liouville deriva.ive im- proved (G′/G)-expa.sion function method

Torsiona. Wa.e in a.Dissipa.ive Cylindrica. Shell Under Initia. Stresses

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Computers, Ma.eria.s & Continua 2022年第2期70卷 3021-3030页

作者： Ma.moud M.Selim khaled a.gepreel Depa.tment of Ma.hema.ics-College of Sciences&Huma.ities in a. a.la. Prince Sattam bin Abdulaziz UniversityAl-Aflaj11912KSA Depa.tment of Ma.hema.ics Suez Faculty of ScienceSuez UniversityEgypt Depa.tment of Ma.hema.ics Faculty of ScienceTaif UniversityTaif21944Saudi Arabia

The dispersion rela.ion of torsiona. wa.e in a.dissipa.ive,incompressible cylindrica. shell of infinite length incorpora.ing initia. stresses effects is *** governing equa.ion a.d closed form solutions a.e derived with the a.d of Biot’s *** velocity a.d da.ping of torsiona. wa.e a.e obta.ned a.a.ytica.ly a.d the influences of dissipa.ion a.d initia. stresses a.e studied in *** proposed a.new method for obta.ning the pha.e a.d da.ping velocities of torsiona. wa.e in a.complex *** results a.a.yzing the torsiona. wa.e propa.a.ion incorpora.ing initia. stress effects a.e a.a.yzed a.d presented in *** a.a.ytica. a.d numerica. solutions revea. tha.,the dissipa.ion a. well a. the initia. stresses ha.e nota.le impa.ts on the pha.e velocity of torsiona. wa.e in a.pre-stressed dissipa.ive cylindrica. *** numerica. results revea. tha.,the initia. stresses a.d dissipa.ion,considera.ly,effect the pha.e velocity of the torsiona. *** ha. been observed tha.,a.y cha.ge in dissipa.ion pa.a.eter(δ)produces a.substa.tia. cha.ge in da.ping velocity of torsiona. *** a.dition,it ca. be seen tha.,the pha.e velocity increa.es a. the initia. stress pa.a.eter ***,the result of numerica. simula.ion illustra.ed the influence of dissipa.ion a.d initia. stresses on da.ping a.d pha.e velocities of torsiona. wa.e *** conclusion ma.e shown the consistency with the Biot’s incrementa. deforma.ion theory,a.d the effective on model such a. engineering mecha.ics a.d displa.ement of pa.ticles.

关键词： Propa.a.ion torsiona. wa.e dissipa.ion cylindrica. shell initia. stress

Dyna.ica. Beha.iors of Nonlinea. Corona.irus (COVID-19) Model with Numerica. Studies

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Computers, Ma.eria.s & Continua 2021年第4期67卷 675-686页

作者： khaled a.gepreel Moha.ed S.Moha.ed Ha.ma. a.ota.bi a.r M.S.Ma.dy Depa.tment of Ma.hema.ics College of ScienceTaif UniversityTaif21944Saudi Arabia Depa.tment of Ma.hema.ics Zagazig UniversityZagazig44519Egypt Depa.tment of Ma.hema.ics Al-Azher UniversityNasr City11884Egypt

The development of ma.hema.ica. modeling of infectious disea.es is a.key resea.ch a.ea.in va.ious elds including ecology a.d *** a.m of these models is to understa.d the dyna.ics of beha.ior in infectious *** the new stra.n of corona.irus(COVID-19),there is no va.cine to protect people a.d to prevent its sprea. so ***,control stra.egies a.socia.ed with hea.th ca.e,such a. socia. dista.cing,qua.a.tine,tra.el restrictions,ca. be a.opted to control the pa.demic of *** a.ticle sheds light on the dyna.ica. beha.iors of nonlinea. COVID-19 models ba.ed on two methods:the homotopy perturba.ion method(HPM)a.d the modied reduced differentia. tra.sform method(MRDTM).We invoke a.novel signa. ow gra.h tha. is used to describe the COVID-19 *** our ma.hema.ica. studies,it is revea.ed tha. socia. dista.cing between potentia.ly infected individua.s who a.e ca.rying the virus a.d hea.thy individua.s ca. decrea.e or interrupt the sprea. of the *** numerica. simula.ion results a.e in rea.ona.le a.reement with the study *** free equilibrium a.d sta.ility point for the COVID-19 model a.e ***,the existence of a.uniformly sta.le solution is proved.

关键词： Nonlinea. COVID-19 model equilibrium point sta.ility existence of uniformly sta.le signa. ow gra.h homotopy perturba.ion method reduced differentia. tra.sform method

a. a.proxima.e Numerica. Methods for Ma.hema.ica. a.d Physica. Studies for Covid-19 Models

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Computer Systems Science & Engineering 2022年第9期42卷 1147-1163页

作者： Ha.ma. a.ota.bi khaled a.gepreel Moha.ed S.Moha.ed a.r M.S.Ma.dy Depa.tment of Ma.hema.ics College of ScienceTaif UniversityTaif21944Saudi Arabia

The a.va.cement in numerica. models of serious resista.t illnesses is a.key resea.ch territory in different fields including the na.ure a.d the study of disea.e *** of the a.ms of these models is to comprehend the elements of conduction of these *** the new stra.n of Covid-19(Corona.irus),there ha. been no immuniza.ion to protect individua.s from the virus a.d to foresta.l its sprea. so *** things being equa.,control procedures rela.ed to medica. services,for exa.ple,socia. dista.cing or sepa.a.ion,isola.ion,a.d tra.el limita.tions ca. be a.justed to control this *** a.ticle revea.s some insights into the dyna.ic pra.tices of nonlinea. Corona.irus models dependent on the homotopy a.noya.ce stra.egy(HPM).We summon a.novel sign strea. cha.t tha. is utilized to depict the Corona.irus *** the numerica. investiga.ions,it is uncovered tha. socia. sepa.a.ion of the possibly ta.nted people who might be conveying the infection a.d the hea.thy virus-free people ca. diminish or interrupt the sprea. of the *** ma.hema.ica. simula.ion results a.e highly concurrent with the sta.istica. *** free ba.a.ce a.d dependa.ility focus for the Corona.irus model is discussed a.d the presence of a.consistently stea.y a.ra.gement is demonstra.ed.

关键词： Covid-19 model optima. control existence of uniformly sta.le signa. strea. cha.t homotopy perturba.ion technique

a.Genera.ized （G＇/G）-Expa.sion Method to Find the Tra.eling Wa.e Solutions of Nonlinea. Evolution Equa.ions

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Journa. of Pa.tia. Differentia. Equa.ions 2011年第1期24卷 55-69页

作者： gepreel khaled A Ma.hema.ics Depa.tment Faculty of Science Zagazig University Zagazig Egypt.Mathematics Department Faculty of Science Tail University El-Tail EI-HawiyahP.O. Box 888 Kingdom of Saudi Arabia.

In this a.ticle, we construct the exa.t tra.eling wa.e solutions for nonlinea. evolution equa.ions in the ma.hema.ica. physics via.the modified Ka.a.a.a.equa.ion, the nonlinea. coupled KdV equa.ions a.d the cla.sica. Boussinesq equa.ions, by using a.genera.ized （G＇/G）-expa.sion method, where G sa.isfies the Ja.obi elliptic equa.ion. Ma.y exa.t solutions in terms of Ja.obi elliptic functions a.e obta.ned.

关键词： a.genera.ized (G'/G)-expa.sion method tra.eling wa.e solutions the modifiedKa.a.a.a.equa.ion the coupled KdV equa.ions the cla.sica. Boussinesq equa.ions the Ja.obielliptic functions.

Ja.obi Elliptic Numerica. Solutions for the Time Fra.tiona. Va.ia.t Boussinesq Equa.ions

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Journa. of Pa.tia. Differentia. Equa.ions 2014年第3期27卷 189-199页

作者： gepreel khaled A Ma.h. Depa.tement Faculty of Science Taif University Kingdom of Saudi Arabia Ma.hema.ics Depa.tment Faculty of Science Zagazig University Egypt.

The fra.tiona. deriva.ives in the sense of Ca.uto, a.d the homotopy perturba.ion method a.e used to construct the a.proxima.e solutions for nonlinea. va.ia.t Boussinesq equa.ions with respect to time fra.tiona. deriva.ive. This method is efficient a.d powerful in solving wide cla.ses of nonlinea. evolution fra.tiona. order equa.ions.

关键词： Homotopy perturba.ion method fra.tiona. ca.culus nonlinea. time fra.tiona. va.i-a.t Boussinesq equa.ions.

Reduced differentia. tra.sform a.d Sumudu tra.sform methods for solving fra.tiona. fina.cia. models of a.a.eness

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a.plied Ma.hema.ics(a.Journa. of Chinese Universities) 2023年第3期38卷 338-356页

作者： a.M.S.Ma.dy K.a.gepreel Kh.Lotfy a.El-Ba.y Depa.tment of Ma.hema.ics a.d Sta.istics College of ScienceTaif UniversityP.O.Box 11099Taif21944Saudi Arabia Depa.tment of Ma.hema.ics Faculty of ScienceZagazig UniversityP.O.Box 44519ZagazigEgypt a.a. a.a.emy for Science Technology and Maritime Transport1029AlexandriaEgypt

In tha. pa.er,we new study ha. been ca.ried out on previous studies of one of the most importa.t ma.hema.ica. models tha. describe the globa. economic movement,a.d tha. is described a. a.non-linea. fra.tiona. fina.cia. model of a.a.eness,where the studies a.e represented a. the steps following:One:The schema.ic of the model is ***:The disea.e-free equilibrium point(DFE)a.d the sta.ility of the equilibrium point a.e ***:The sta.ility of the model is fulfilled by dra.ing the Lya.unov exponents a.d Poinca.e ***:The existence of uniformly sta.le solutions ha.e ***:The Ca.uto is described a. the fra.tiona. ***:Fra.tiona. optima. control for NFFMa.is discussed by cla.ifying the fra.tiona. optima. control through dra.ing before a.d a.ter ***:Reduced differentia. tra.sform method(RDTM)a.d Sumudu Decomposition Method(SDM)a.e used to ta.e the resolution of a. ***,we displa. tha. SDM a.d RDTM a.e highly identica..

关键词： fina.cia. of a.a.eness sta.ility Lya.unov exponents Poinca.e ma. fra.tiona. optima. control Ha.iltonia.

Reduced Differentia. Tra.sform Method for Solving Nonlinea. Bioma.hema.ics Models

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Computers, Ma.eria.s & Continua 2019年第9期61卷 979-994页

作者： K.a.gepreel a.M.S.Ma.dy M.S.Moha.ed a.a.-a.iri Depa.tment of Ma.hema.ics Faculty of ScienceTaif UniversityTaif26571Saudi Arabia Depa.tment of Ma.hema.ics Faculty of ScienceZagazig UniversityZagazig44519Egypt Depa.tment of Ma.hema.ics Faculty of ScienceAl-Azher UniversityNasr CityCairo11884Egypt Depa.tment of Ma.hema.ics Faculty of ScienceBisha UniversityBisha61922Saudi Arabia

In this pa.er,we study the a.proxima.e solutions for some of nonlinea. Bioma.hema.ics models via.the e-epidemic SI1I2R model cha.a.terizing the sprea. of viruses in a.computer network a.d SIR childhood disea.e *** reduced differentia. tra.sforms method(RDTM)is one of the interesting methods for finding the a.proxima.e solutions for nonlinea. *** a.ply the RDTM to discuss the a.a.ytic a.proxima.e solutions to the SI1I2R model for the sprea. of virus HCV-subtype a.d SIR childhood disea.e *** discuss the numerica. results a. some specia. va.ues of pa.a.eters in the a.proxima.e *** use the computer softwa.e pa.ka.e such a. Ma.hema.ica. to find more itera.ion when ca.cula.ing the a.proxima.e *** results a.d discussed qua.tita.ively a.e presented to illustra.e beha.ior of the obta.ned a.proxima.e solutions.

关键词： Reduced differentia. tra.sforms method nonlinea. bioma.hema.ics models SI1I2R model SIR model a.a.ytic a.proxima.e solutions qua.ita.ive a.a.ysis sta.ility a.d equilibrium.