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Related Experiment Video

Updated: Jun 21, 2026

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

R-function relationships for application in the fractional calculus.

Carl F Lorenzo¹, Tom T Hartley

¹National Aeronautics and Space Administration, Glenn Research Center, Cleveland, Ohio, USA.

Critical Reviews in Biomedical Engineering

|August 4, 2009

Summary

This summary is machine-generated.

This study explores the R-function, a generalization of the F-function crucial for fractional calculus. It details R-function relationships with exponential functions and their fractional derivatives, aiding fractional differential equation analysis.

Related Experiment Videos

Last Updated: Jun 21, 2026

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Area of Science:

Mathematics
Fractional Calculus

Background:

The F-function and R-function are vital in fractional calculus.
These functions generalize the exponential function for solving fractional differential equations.

Purpose of the Study:

To investigate the intrarelationships of the R-function.
To establish connections between the R-function and the exponential function (e^t).

Main Methods:

Analyzing relationships between the R-function and the exponential function.
Deriving fractional derivatives of the exponential function.
Developing inverse relationships of the exponential function in terms of the R-function.

Main Results:

Established various intrarelationships of the R-function.
Demonstrated connections between the R-function, the exponential function, and their fractional derivatives.
Derived approximations for the R-function and its inverse relationships.

Conclusions:

The explored relationships and approximations of the R-function are valuable for further analysis in fractional calculus.
This work enhances the understanding of fundamental functions in fractional differential equations.