分?jǐn)?shù)階微分方程迭代方法

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1、2009–4–30AnIterativeMethodforFractionalOrderDi?erentialEquationsCandidateSupervisorandRankYapingZhangProfessorXuenianCaoCollegeProgramSpecializationDegreeUniversityDateMathematicsandComputationalScienceTheComputationalMathematicsNumericalMethodsofFraction

2、alDi?erentialEquationsMasterofScienceXiangTanUniversityApril30th,2009NIM)Daftardar?GejjiBagley?Torvik-(ADM)Jafari(VIM)I(HPM)(AdomianAbstractFractionaldi?erentialequationscane?ectivelysimulatemanyscienti?cphenomenaincontrollerstheory,?uidmechanics,biolog

3、y,andhasbeenusedwidelyinscienti?candengineering?eld.Inrecentyears,moreandmoreschol-arsresearchinfractionaldi?erentialequations,theytriedtoresolvefractionaldi?erentialequations,butmanyanalyticsolutionsoffractionaldi?erentialequationsareexpressedbycomplexseri

4、esorspecialfunctions,sothenumer-icalsolutionoffractionaldi?erentialequationsbecomesmoreimportant.Inthispaper,anewiterativemethod(NIM)proposedbyDaftarar-GejjiandJafariisappliedtosolvefractionalordinarydi?erentialequationsandfractionalpartialdi?erentialequati

5、ons.WeobtainthenumericalsolutionsoffractionalorderBagley-Torvikequation,nonlinearanomalousdi?usionequa-tion,linearandnonlineartime-spacefractionalreaction-di?usionequationsandfractionaltelegraphequation.Numericalresultsdemonstratethee?-ciencyofthisiterative

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