Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

Luchko, Yury, and Trujillo, Juan. "Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative." Fractional Calculus and Applied Analysis 10.3 (2007): 249-267. <http://eudml.org/doc/11329>.

@article{Luchko2007,
abstract = {2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones. Whereas the Riemann-Liouville definition of a fractional derivative is usually employed in mathematical texts and not so frequently in applications, and the Grünwald-Letnikov definition – for numerical approximation of both Caputo and Riemann-Liouville fractional derivatives, the Caputo approach appears often while modeling applied problems by means of fractional derivatives and fractional order differential equations. In the mathematical texts and applications, the so called Erdélyi-Kober (E-K) fractional derivative, as a generalization of the Riemann-Liouville fractional derivative, is often used, too. In this paper, we investigate some properties of the Caputo-type modification of the Erdélyi-Kober fractional derivative. The relation between the Caputo-type modification of the E-K fractional derivative and the classical E-K fractional derivative is the same as the relation between the Caputo fractional derivative and the Riemann-Liouville fractional derivative, i.e. the operations of integration and differentiation are interchanged in the corresponding definitions. Here, some new properties of the classical Erdélyi-Kober fractional derivative and the respective ones of its Caputo-type modification are presented together.},
author = {Luchko, Yury, Trujillo, Juan},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 33E12; 33E30; 44A15; 45J05},
language = {eng},
number = {3},
pages = {249-267},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative},
url = {http://eudml.org/doc/11329},
volume = {10},
year = {2007},
}

TY - JOUR
AU - Luchko, Yury
AU - Trujillo, Juan
TI - Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative
JO - Fractional Calculus and Applied Analysis
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 3
SP - 249
EP - 267
AB - 2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones. Whereas the Riemann-Liouville definition of a fractional derivative is usually employed in mathematical texts and not so frequently in applications, and the Grünwald-Letnikov definition – for numerical approximation of both Caputo and Riemann-Liouville fractional derivatives, the Caputo approach appears often while modeling applied problems by means of fractional derivatives and fractional order differential equations. In the mathematical texts and applications, the so called Erdélyi-Kober (E-K) fractional derivative, as a generalization of the Riemann-Liouville fractional derivative, is often used, too. In this paper, we investigate some properties of the Caputo-type modification of the Erdélyi-Kober fractional derivative. The relation between the Caputo-type modification of the E-K fractional derivative and the classical E-K fractional derivative is the same as the relation between the Caputo fractional derivative and the Riemann-Liouville fractional derivative, i.e. the operations of integration and differentiation are interchanged in the corresponding definitions. Here, some new properties of the classical Erdélyi-Kober fractional derivative and the respective ones of its Caputo-type modification are presented together.
LA - eng
KW - 26A33; 33E12; 33E30; 44A15; 45J05
UR - http://eudml.org/doc/11329
ER -