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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.
- 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