Euler-Lagrange-Hamilton Dyna micswith Fractional Action
Keywords:
fractionalStieltjesaction,Euler-LagrangeorHamiltonequations,dynamicconnection,symplectic manifold.Abstract
Our aimis three-fold: topoin toutthatthe fractio nalinteg ralactionsa recomingfro mStieltjes actions,to findtheroot sandthege ometryofsom eEuler-Lagra ngeorHamilt onODEsorPDEs,t oev identiateso me ideasthat includethe fractaltheoryof solids.Section 1discussest heEuler-LagrangeODEsassociat edtosingle -timeStieltjes actions.Teirdu alHamilton ODEsarea nalizedin Section2.Section3studies thegeo metryas sociatedtosin gle-timeEul er-Lagrang eorHamilto noperators .Section4ana lyzestheEuler-LagrangePDEsassociatedtomultitime Stieltjesactions(multipleorcurvilinearintegrals).Section5formulatesthemultitimeperimetricproblemofnon-renewableresources.Section6studiestheHamiltonPDEsassociatedtomultitimeStieltjesactions.Section7 describesthegeometryassociatedtomultitimeEuler-LagrangeorHamiltonoperators(dynamicalconnectionand semi-spray,Poincar´e-Cartanform,Hamilton-Poissonsystemsonjetbundle).Section8formulatesamultitime Hamilton-Poissonsystemstheoryonjetbundle.
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