On the definition of fractional derivatives in rheology
On the definition of fractional derivatives in rheology作者机构：Department of Engineering Mechanics Tsinghua University Beijing 100084 ChinaDepartment of Physics the Chinese University of Hong Kong Hong Kong China
出 版 物：《Theoretical & Applied Mechanics Letters》 (力学快报（英文版）)
年 卷 期：2011年第1卷第1期
页 面：62-65页
学科分类：07[理学] 070101[理学-基础数学] 0831[工学-生物医学工程（可授工学、理学、医学学位）] 0830[工学-环境科学与工程（可授工学、理学、农学学位）] 0707[理学-海洋科学] 0815[工学-水利工程] 0805[工学-材料科学与工程（可授工学、理学学位）] 0813[工学-建筑学] 0824[工学-船舶与海洋工程] 0802[工学-机械工程] 0836[工学-生物工程] 0814[工学-土木工程] 0825[工学-航空宇航科学与技术] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学]
基 金：supported by NSFC under the grant number 10972117
主 题：fractional derivative Caputo definition Riemann-Liouville definition Scott-Blair model
摘 要：During the last two decades fractional calculus has been increasingly applied to physics, especially to *** is well known that there are obivious differences between Riemann-Liouville (R-L) definition and Caputo definition,which are the two most commonly used definitions of fractional *** multiple definitions of fractional derivatives have hindered the application of fractional calculus in *** this paper,we clarify that the R-L definition and Caputo definition are both Theologically unreasonable with the help of the mechanical analogues of the fractional element *** also find that to make them more reasonable Theologically,the lower terminals of both definitions should be put to—∞.We further prove that the R-L definition with lower terminal—∞and the Caputo definition with lower terminal—∞are equivalent in the differentiation of functions that are smooth enough and functions that have finite number of singular *** we can define the fractional derivatives in rheology as the R-L derivatives with lower terminal—∞(or,equivalently,the Caputo derivatives with lower terminal—∞) not only for steady-state processes,but also for transient processes.
维普期刊数据库
同方期刊数据库