arXiv subjects
Publications and source records attributed to Fikret A. Aliev.
In this paper the Mittag-Leffler function is given through the exponential functions for any rational derivatives of m/n order, where m 1 are natural irreducible numbers (if n=1 then m is also equal to unity). Unlike the previous papers the given formulas do not contain integrals.
An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in this case does not have constant matrix coefficients. Further, this method is compared with the known approximate method. The above scheme is developed for arbitrary linear systems with piecewise constant perturbations. The results are applied to the discretization of linear controlled systems and are illustrated with numerical examples.
The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding solution. On the basis of the obtained results the conditions are given, providing the asymptotic stability of the initial system. The results are illustrated on the numerical example, where it is shown that when the order of the fractional derivative tends to unity, so the solution tends to the corresponding exponential function.
In this work at first the relation the Mittag-Lefler function to the exponential is given. The results are applied to the construction of the solution of Cauchy problem for ordinary linear operator differential equations with constant coefficients and fractional derivatives. On the example is shown that when the order of the derivatives (fractional) approaches to integers the results coincide with the classical.