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Critical Reviews™ in Biomedical Engineering

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ISSN Печать: 0278-940X

ISSN Онлайн: 1943-619X

SJR: 0.262 SNIP: 0.372 CiteScore™:: 2.2 H-Index: 56

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R-Function Relationships for Application in the Fractional Calculus

Том 36, Выпуск 1, 2008, pp. 57-78
DOI: 10.1615/CritRevBiomedEng.v36.i1.50
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Краткое описание

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.

ЦИТИРОВАНО В
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