INITIALIZATION OF FRACTIONAL DIFFERENTIAL EQUATIONS: BACKGROUND AND THEORY

机译：分数阶微分方程的初始化：背景和理论

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It has been known that the initialization of fractional operators requires time-varying functions, a complicating factor. This paper simplifies the process of initialization of fractional differential equations by deriving Laplace transforms for the initialized fractional integral and derivative that generalize those for the integer-order operators. This paper provides background on past work in the area and determines the Laplace transforms for initialized fractional integrals of any order and fractional derivatives of order less than one. A companion paper in this conference extends the theory to higher order derivative operators and provides application insight.

机译：众所周知，分数运算符的初始化需要时变函数，这是一个复杂的因素。本文通过为初始化后的分数积分和导数推导Laplace变换，从而简化了分数阶微分方程的初始化过程，从而对整数阶算子进行了推广。本文提供了该区域过去工作的背景，并确定了任意阶数的初始化分数积分和阶数小于1的分数导数的Laplace变换。本次会议的一篇论文将理论扩展到高阶导数算子，并提供了应用程序见解。

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来源
《ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2007》|2007年|P.13251333|共2页
会议地点 Las VegasNV(US);Las VegasNV(US);Las VegasNV(US)
作者
Carl F. Lorenzo; Tom T. Hartley;
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作者单位

NASA Glenn Research Center Cleveland, Ohio 44135;

University of Akron Akron, Ohio 44325-3904;

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会议组织
原文格式 PDF
正文语种 eng
中图分类柔性制造系统及柔性制造单元;
关键词
fractional differential equations; fractional operators; initialization; laplace transforms;

机译：分数阶微分方程;分数维算子;初始化;拉普拉斯变换;

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INITIALIZATION OF FRACTIONAL DIFFERENTIAL EQUATIONS: BACKGROUND AND THEORY

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