국내 최대 기계 및 로봇 연구정보

기술보고서

기술보고서 게시판 내용
타이틀	Generalized Functions for the Fractional Calculus
저자	Carl F. Lorenzo and Tom T. Hartley
Keyword	Fractional calculus; Fractional differential equations; Systems; Generalized functions; Eigenfunctions
URL	http://gltrs.grc.nasa.gov/reports/1999/TP-1999-209424-REV1.pdf
보고서번호	NASA TP-1999-209424-REV1
발행년도	1999
출처	NASA Glenn Research Center
ABSTRACT	Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler function Eq[atq] (1903a, 1903b, 1905), and the F-function Fq[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.