On physical interpretations of fractional integration and differentiation
The paper deals with physical interpretation of fractional integration and differentiation in the Riemann-Liouville form [see Sections 2 and 6 in the book by \textit{S. G. Samko}, \textit{A. A. Kilbas} and \textit{O. I. Marichev}: ``Fractional integrals and derivatives: Theory and applications'' (Russian, 1987; Zbl 0617.26004; English translation, 1993; Zbl 0818.26003)]. The problem, when a fractional order system can be represented by a causal dynamic model, is under consideration. The known models of such a kind are discussed, and a new model is presented: fractional integration and differentiation are realized as the linear dynamical systems \[ {dz(x)\over dx}= A(x) z(x)+ Bh(x),\quad f(x)= C(x)z(x), \] and \[ {dz(x)\over dx}= P(x) z(x)+ Q(x) f(x),\quad h_n(x)= R(x) z(x)+ S(x) f(x), \] with \(x\) as a time variable, respectively. In this way, regularization of fractional integration and differentiation is studied, asymptotic error estimates and simulation results are given.
fractional integration and differentiation
scientific article; zbMATH DE number 1120308