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The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equation.

The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equation.

Authors :
Sabatier, Jocelyn
Agrawal, Om Prakash
Machado, J. A. Tenreiro
Achar, B. N. Narahari
Lorenzo, Carl F.
Hartley, Tom T.
Source :
Advances in Fractional Calculus; 2007, p27-42, 16p
Publication Year :
2007

Abstract

Recognizing the importance of proper initialization of a system, which is evolving in time according to a differential equation of fractional order, Lorenzo and Hartley developed the method of properly incorporating the effect of the past (history) by means of an initialization function for the Riemann-Liouville and the Grunwald formulations of fractional calculus. The present work addresses this issue for the Caputo fractional derivative and cautions that the commonly held belief that the Caputo formulation of fractional derivatives properly accounts for the initialization effects is not generally true when applied to the solution of fractional differential equations. Key words Caputo fractional derivatives, initialization issues. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISBNs :
9781402060410
Database :
Supplemental Index
Journal :
Advances in Fractional Calculus
Publication Type :
Book
Accession number :
33094028
Full Text :
https://doi.org/10.1007/978-1-4020-6042-7_3