ISBN-10: 1634827422

ISBN-13: 9781634827423

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Das Nachschlagewerk f? r Studium und Beruf stellt wichtige Zusammenh? nge und Formeln der Mathematik, Physik, Chemie sowie die Grundlagen der Technik dar. Ebenfalls ber? cksichtigt werden die Gebiete der Optoelektronik, Nachrichtentechnik und Informatik. H? ufig gebrauchte Stoffwerte, Konstanten und Umrechnungen von Einheiten sowie die Eigenschaften der chemischen Elemente sind f?

Via the particular research of the fashionable improvement of the mechanics of deformable media are available the deep inner contradiction. From the single hand it truly is declared that the deformation and fracture are the hierarchical strategies that are associated and unite numerous structural and scale degrees. From the opposite hand the sequential research of the hierarchy of the deformation and destruction isn't really performed.

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The present contribution is organized as follows. We shall firstly bear in mind the essential of modified Riemann-Liouville derivative and of fractional difference, and then we shall directly calculate the Z-transform of the later, and by this way we shall cross over modified Ztransform. Therefore we shall have some suggestions to get a modelling for anticipatory systems which exhibit long-range memory effects. After some background on our modelling of fractional Gaussian white noise, we shall derive its Z-transform considered as a Gaussian random variable with given mean value and given variance.

Mainly we shall improve its derivation and clarify the effects of non-differentiability in the result. And to conclude, we shall outline some prospects for the application of fractional derivative to generalized functions. This present theory is a theory for non-differentiable functions, like for instance those functions which could be considered as generated by random noises, and a prospect for future research would be to examine whether white noises could not be considered as elemental processes in this approach.

1) F( ) ( z )  j 0  F ( z, T )    z  j F ( z, T ) j j   (1) j 0    z  j , j j that is to say F( ) ( z )  (1  z 1 ) F ( z, T ) . 5) Further Remarks and Comments Remark 1. If we notice that one has the equality 1  z  1       Z  (1) t    , T  1 , t   we come across the convolution F( ) ( z )  1  z  1  F ( z,  ), T  1      Z  (1) t    f (t   )  , T  1. 6) Remark 2. 7) and at first glance this relation appears to be an excellent support to an alternative for defining fractional derivative via fractional difference.