Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

Mainardi, Francesco, and Gorenflo, Rudolf. "Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey." Fractional Calculus and Applied Analysis 10.3 (2007): 269-308. <http://eudml.org/doc/11330>.

@article{Mainardi2007,
abstract = {2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classica theory of linear viscoelasticity, we contrast these two types of fractiona derivatives in their ability to take into account initial conditions in the constitutive equations of fractional order. We also provide historical notes on the origins of the Caputo derivative and on the use of fractional calculus in viscoelasticity.},
author = {Mainardi, Francesco, Gorenflo, Rudolf},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 33E12; 33C60; 44A10; 45K05; 74D05},
language = {eng},
number = {3},
pages = {269-308},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey},
url = {http://eudml.org/doc/11330},
volume = {10},
year = {2007},
}

TY - JOUR
AU - Mainardi, Francesco
AU - Gorenflo, Rudolf
TI - Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey
JO - Fractional Calculus and Applied Analysis
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 3
SP - 269
EP - 308
AB - 2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classica theory of linear viscoelasticity, we contrast these two types of fractiona derivatives in their ability to take into account initial conditions in the constitutive equations of fractional order. We also provide historical notes on the origins of the Caputo derivative and on the use of fractional calculus in viscoelasticity.
LA - eng
KW - 26A33; 33E12; 33C60; 44A10; 45K05; 74D05
UR - http://eudml.org/doc/11330
ER -