分数阶微分方程迭代方法

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1、2009–4–30AnIterativeMethodforFractionalOrderDifferentialEquationsCandidateSupervisorandRankYapingZhangProfessorXuenianCaoCollegeProgramSpecializationDegreeUniversityDateMathematicsandComputationalScienceTheComputationalMathematicsNumericalMethodsofFraction

2、alDifferentialEquationsMasterofScienceXiangTanUniversityApril30th,2009NIM)Daftardar−GejjiBagley−Torvik-(ADM)Jafari(VIM)I(HPM)(AdomianAbstractFractionaldifferentialequationscaneffectivelysimulatemanyscientificphenomenaincontrollerstheory,fluidmechanics,biolog

3、y,andhasbeenusedwidelyinscientificandengineeringfield.Inrecentyears,moreandmoreschol-arsresearchinfractionaldifferentialequations,theytriedtoresolvefractionaldifferentialequations,butmanyanalyticsolutionsoffractionaldifferentialequationsareexpressedbycomplexseri

4、esorspecialfunctions,sothenumer-icalsolutionoffractionaldifferentialequationsbecomesmoreimportant.Inthispaper,anewiterativemethod(NIM)proposedbyDaftarar-GejjiandJafariisappliedtosolvefractionalordinarydifferentialequationsandfractionalpartialdifferentialequati

5、ons.WeobtainthenumericalsolutionsoffractionalorderBagley-Torvikequation,nonlinearanomalousdiffusionequa-tion,linearandnonlineartime-spacefractionalreaction-diffusionequationsandfractionaltelegraphequation.Numericalresultsdemonstratetheeffi-ciencyofthisiterative

6、methodbycomparingseveralnumericalmethods,suchasAdomiandecompositionmethod(ADM),variationaliterationmethod(VIM)andhomotopyperturbationmethod(HPM).Keywords:Fractionalorderderivatives;Fractionalorderintegrals;Frac-tionalorderdifferentialequations;Newiterativeme

7、thodII1§1.1§1.2...........................................................136§2.1(NIM).....................6§2.2.............................712§3.1NIM§3.2...........12.............................14-20§4.1NIM§4.2NIM--.........20.......2329§5.1N

8、IM§5.2...................29.............................303435i§1.1Leibniz(1695)(1823Euler(1730)Liouville(1832)Laplace(1812)Riemann(1847)Fourier(1822))AbelNutting([29])(1921)Gemant([25][26])(19