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1、Commun.Theor.Phys.67(2017)9–14Vol.67,No.1,January1,2017NewExactSolutionsofTimeFractionalGardnerEquationbyUsingNewVersionofF-ExpansionMethodYusufPandir∗andHasanHuseyinDuzgun†DepartmentofMathematics,BozokUniversity,66100,Yozgat,Turkey(ReceivedMay31,2016
2、;revisedmanuscriptreceivedNovember2,2016)AbstractInthisarticle,weconsideranalyticalsolutionsofthetimefractionalderivativeGardnerequationbyusingthenewversionofF-expansionmethod.WiththisproposedmethodmultipleJacobiellipticfunctionsaresituatedinthesoluti
3、onfunction.Asaresult,variousexactanalyticalsolutionsconsistingofsingleandcombinedJacobiellipticfunctionssolutionsareobtained.PACSnumbers:02.30.Jr,02.70.Wz,04.20.JbDOI:10.1088/0253-6102/67/1/9Keywords:newversionofF-expansionmethod,nonlineardifferentiale
4、quationswithfractionalderivatives,singleandcombinedJacobiellipticfunctionssolutions1Introductiontionaldifferentialequationssuchaslocalfractionalvaria-tionaliterationmethod,[21]thefractionalfunctionalvari-Withknowledgeofthephysicalanddynamicproper-ablem
5、ethod,[22]localfractionalAdomiandecompositiontiesofthesystemthatexistsinnaturecanbemadeeas-method,[23−24]localfractionalFourierseriesmethod,[25]ilypredictionsaboutthecurrentandfuturefunctioning.finitedifferencemethod,[26]finiteelementmethod[27]andThesepr
6、opertiesareneededtoidentifyfractionalderiva-tivesandintegrals.Manyeventsinthephysicalsystemsoon.Therestofthepaperisorganizedasfollows:Incanbeexplainedusingfractionalorderequations.Frac-Sec.2somebasicdefinitionsoffractionalderivativeshavetionalorderpart
7、ialdifferentialequationsareusedtoob-beengiven.AlsodevelopednewversionsofF-expansiontainsolutionstoproblemsthathaveariseninanumbermethodforfractionaldifferentialequationshavebeenpre-ofdifferentareas,suchasdynamics,engineering,physics,sented.TheninSec.3wea
8、pplyproposedmethodtotimechemistry,biology,signalprocessing,systemidentifica-fractionalderivativenonlinearGardnerequation.Thepa-tion,continuummechanics,electromagnetics,controlthe-perendsinSec.4withconclusion.ory.Therearedifferentkindsoffractiona
