... 26) From (24), we have d 1 m 1 (m) (t ), (27) a D f(t ) = Dt a Jt Dt f(t ) = Dt a Jt f dt t where a Jt is the fractional ... 1 ( ) -1 f (m) (a ) +1 t (m+1) ( ) Substitution of (28)into(27) proves (23). (t ) + f (m) (a ) = a D f(t ) + t -1 ( ) f (m) (a ...
... m=- mn 3 for all n. If 3 cannot be satisfied, we must define E un , um = un - um ... The interaction term in 21 is + n=- + + + + + 27 e m=- mn -ikn x J n, m un - u m = n ...
... k , 27 in the space of continuously differentiable functions x t If nT t n +1 T, then Eq. 27 gives m-1 C xt = k=0 x0k k KT t- k! m t - kT k=1 -1 G x kT . ...
... fractional generalization of Eq. 27 in the form 011102-3 VASILY E. TARASOV PHYSICAL REVIEW E 71, 011102 2005 r -1 0 M r= 2 d=V ... Lett. 45, 149 1999 . 27M. E. Tuckerman, Y. Liu, G. Ciccotti, and G. J. Martyna, J. Chem. Phys. 115, 1678 2001 . ...
... 26 27 28 M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 1993 . L. M. Pismen, Vortices in Nonlinear Fields Oxford Science, Oxford, 1999 . ...
... 27] V.M. Agranovich, V.L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons, Interscience Publishers, John Wiley and Sons, 1966, p. 316. ...