국내 최대 기계 및 로봇 연구정보

기술보고서

기술보고서 게시판 내용
타이틀	Initialization, Conceptualization, and Application in the Generalized Fractional Calculus
저자	Carl F. Lorenzo and Tom T. Hartley
Keyword	Generalized calculus; Fractional calculus; Fractional order systems; Calculus; Laplace Transform; Electrochemistry; Filtering; Creep; Viscoelasticity; Semi-infinite systems; Initialization function;
URL	http://gltrs.grc.nasa.gov/reports/1998/TP-1998-208415.pdf
보고서번호	NASA TP-1998-208415
발행년도	1998
출처	NASA Glenn Research Center
ABSTRACT	This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.