Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Order-distributions and the Laplace-domain logarithmic operator | Hartley and Lorenzo Advances in Difference Equations 2011 2011 59 http content 2011 1 59 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Order-distributions and the Laplace-domain logarithmic operator Tom T Hartley1 and Carl F Lorenzo2 Correspondence thartley@ department of Electrical and Computer Engineering University of Akron Akron OH 44325-3904 USA Full list of author information is available at the end of the article Springer Abstract This paper develops and exposes the strong relationships that exist between timedomain order-distributions and the Laplace-domain logarithmic operator. The paper presents the fundamental theory of the Laplace-domain logarithmic operator and related operators. It is motivated by the appearance of logarithmic operators in a variety of fractional-order systems and order-distributions. Included is the development of a system theory for Laplace-domain logarithmic operator systems which includes time-domain representations frequency domain representations frequency response analysis time response analysis and stability theory. Approximation methods are included. Keywords Order-distribution Laplace transform Fractional-order systems Fractional calculus Introduction The area of mathematics known as fractional calculus has been studied for over 300 years 1 . Fractional-order systems or systems described using fractional derivatives and integrals have been studied by many in the engineering area 2-9 . Additionally very readable discussions devoted to the mathematics of the subject are presented by Oldham and Spanier 1 Miller and Ross 10 Oustaloup 11 and Podlubny 12 . It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional-order system theory. Specific applications are viscoelastic materials 13-16 electrochemical processes 17 18 long lines 5 dielectric polarization 19 colored noise 20 soil
