ライブラリ登録: Guest
Begell Digital Portal Begellデジタルライブラリー 電子書籍 ジャーナル 参考文献と会報 リサーチ集
Critical Reviews™ in Biomedical Engineering
SJR: 0.26 SNIP: 0.375 CiteScore™: 1.4

ISSN 印刷: 0278-940X
ISSN オンライン: 1943-619X

Critical Reviews™ in Biomedical Engineering

DOI: 10.1615/CritRevBiomedEng.v36.i1.50
pages 57-78

R-Function Relationships for Application in the Fractional Calculus

Carl F. Lorenzo
National Aeronautics and Space Administration, Glenn Research Center, Cleveland, Ohio, USA
Tom T. Hartley
Department of Electrical and Computer Engineering, University of Akron, USA

要約

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis.
Relationships of the R-function to the common exponential function, et, and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, et, in terms of the R-function are developed. Also, some approximations for the R-function are developed.


Articles with similar content:

Changes in Apparent Rates of Receptor Binding in the Intact Brain in Relation to the Heterogeneity of Reaction Environments
Critical Reviews™ in Neurobiology, Vol.13, 1999, issue 2
Antony Gee, Osamu Inoue, Kaoru Kobayashi
SOME PERSPECTIVES ON PRESSURE-STRAIN CORRELATION MODELING
TSFP DIGITAL LIBRARY ONLINE, Vol.2, 2001, issue
Sharath S. Girimaji
Transformations which leave statistics of the distance of multi particle dynamics to be invariant for isotropic turbulence
ICHMT DIGITAL LIBRARY ONLINE, Vol.0, 2012, issue
V. N. Grebenev, Martin Oberlack
Algorithm for Constructing Voronoi Diagrams with Optimal Placement of Generator Points Based on Theory of Optimal Set Partitioning
Journal of Automation and Information Sciences, Vol.52, 2020, issue 3
Elena M. Kiseleva, Olga M. Prytomanova , Lyudmila L. Hart
Solving the Safe Problem on Matrixes with Two Types of Locks
Journal of Automation and Information Sciences, Vol.47, 2015, issue 2
Aghaei Agh Ghamish Yaghaub