Generalized Caputo Fractional Differential Equations and its Applications

Abstract

This thesis has been divided into six chapters. The firstchapterisanintroduc- tory chapter.Thesecondchapterdealswithdevelopmentofthenewiterativemethodto solvegeneralizedCaputofractionaldi_erential equationsandusingdevelopedmethod solution ofwellknownfractionaldi_erential equationsareobtainedsuchaslinearand nonlinear populationdi_usion equations,Fokker-Plancklinear/non linearfractionaldif- ferential equationsandsomebiologicalpopulationmodels.Thethirdchapterconcerns with developmentofnewiterativemethodtosolvesystemofgeneralisedCaputopartial fractional di_erential equations.Thischapteralsocontainsolutionofsystemofpartial fractional di_erential equationusingdevelopedmethod.Thefourthchapterdiscussed study regardingfractionaldi_erential equationsofelectromagneticwaveswithgeneral- ized Caputofractionalderivativesinplasmaanddielectricmediawhichshowsthatthe electromagnetic fieldschangewithdi_erent fractionalorders.Thefifthchaptercontain study offractionalMaxwellmodelofviscoelasticmaterials,whichareageneralization of classicMaxwellmodeltonon-integerorderderivatives.Theresearcherpresented and discussedformulationsofthefractionalorderviscoelasticmodelandgavephysi- cal interpretationsofthemodelbyusingviscoelasticfunctions.Theresearcherapplied the generalisedCaputofractionalderivativetoviscoelasticmodelsnamelyfractional Maxwell model,fractionalKelvin-VoigtmodelandfractionalZenermodel.Thestress relaxation moduleandcreepcomplianceforeachmodelwerederivedanalyticallyus- ing generalisedCaputofractionalderivative.Theresearcheranalysede_ect offractional order _ and newlyintroducedparameter _ in allthesemodels.Theresultshowsanef- fect onviscoelasticmodelsusingfractionaloperator.Inthelastchapter,theresearcher studied Newton slawofcoolingwithvariousfractionaloperatorswithconstantand variableordersandalsocomparedresultwithexperimentaldataandobtainederrorto check e_ciencyofvariousfractionaloperatorforvarioussubstance. V newline newline newline newline