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页数:28页
时间:2020-03-20
《有关causal算子的分数阶微分方程.pdf》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
1、中文摘要带有causal算子的函数方程能够把常微分方程,积分微分方程,有限或无穷时滞微分方程,Volterra积分方程和中立型微分方程诸如此类微分方程进行有机的统一,在工程等技术领域具有广泛的应用,因此,近年来得到很大的发展.分数阶微积分理论是经典微积分理论的推广,分数阶微分方程在对具有记忆性或者遗传性的动力系统的描述具有独特的优势,随着分数阶微积分,分数阶微分方程在描述物理系统的动力学行为,生物工程,动力系统,控制系统,信号处理等许多科学领域显现出的应用前景,这一方向得到了莲勃发展及广泛研究,已成为当前非线性分析领域的一个研究热点.具我们所
2、知,在Banach空间带有causal算子的分数阶微分方程并没有被广泛研究,我们有必要研究带有causal算子的分数阶微分方程.本文主要研究Banach空间中~类有限时滞非线性causal分数阶微分方程。D8u(t)=(Q甜)(f),a.elt∈[0,T】,Uh,0】29∈C。,其中。D。为Caputo分数阶导数,00为常数,G=c([-o-,0】;x)为连续函数空间,以及一类无穷时滞非线性causal分数阶微分方程DoY(t)=f(t,Y,),t∈[0,T】,O<
3、a4、ityofunifyingordinarydifferentialequations,integrodifferentialequations,differentialequationswithfiniteorinfinitedelay,Valeraintegralequations,andneuralfuncfionalequations.tonamebutafew.ThestudyoffunctionalequationswithcausaloperatorshasbeenrapiddevelopmentinthepastfeWyears5、.FractionalcalculusiSthegeneralizationofclassicalcalculus,andfractionaldifferentialequationshaveuniqueadvantageondescribingthosesystems而t11memoryorhereditarysuchasbiologicalengineering,dynamicsystem,controlsystem,signalprocessingandSOon.Forthisreason,scientistshavemoreinter6、estinginfractionaldifferentialequationsrecentyears.Toourknowledge,fractionalfunctionaldifferentialequationswithcausaloperatorsinBanatspaceshavenotbeenstudiedextensively.Motivatedbythis,westudysomefractionaldifferentialequationswithcausaloperators.Thisthesismainlystudiesacla7、ssofnonlinearcausalfractionaldifferentialequationswithfinitedelayinBanachspaces。Da“(,)=(Q“)(f),a.e.t∈【0,T】,甜L’o】=9∈C。,where。D“istheCaputofractionalderivativeoforder0<仅<1,O:C(【0,丁】;X)专Lq([o,丁】;X)isacausaloperator,T>0,C。=C(卜仃,O];X),aswellasaclassofinfinitedelaynonlinearcausal8、fractionaldifferentialequationDoy(t)=f(t,儿),t∈[0,T】,O
4、ityofunifyingordinarydifferentialequations,integrodifferentialequations,differentialequationswithfiniteorinfinitedelay,Valeraintegralequations,andneuralfuncfionalequations.tonamebutafew.ThestudyoffunctionalequationswithcausaloperatorshasbeenrapiddevelopmentinthepastfeWyears
5、.FractionalcalculusiSthegeneralizationofclassicalcalculus,andfractionaldifferentialequationshaveuniqueadvantageondescribingthosesystems而t11memoryorhereditarysuchasbiologicalengineering,dynamicsystem,controlsystem,signalprocessingandSOon.Forthisreason,scientistshavemoreinter
6、estinginfractionaldifferentialequationsrecentyears.Toourknowledge,fractionalfunctionaldifferentialequationswithcausaloperatorsinBanatspaceshavenotbeenstudiedextensively.Motivatedbythis,westudysomefractionaldifferentialequationswithcausaloperators.Thisthesismainlystudiesacla
7、ssofnonlinearcausalfractionaldifferentialequationswithfinitedelayinBanachspaces。Da“(,)=(Q“)(f),a.e.t∈【0,T】,甜L’o】=9∈C。,where。D“istheCaputofractionalderivativeoforder0<仅<1,O:C(【0,丁】;X)专Lq([o,丁】;X)isacausaloperator,T>0,C。=C(卜仃,O];X),aswellasaclassofinfinitedelaynonlinearcausal
8、fractionaldifferentialequationDoy(t)=f(t,儿),t∈[0,T】,O
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