# Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

Mainardi, Francesco; Gorenflo, Rudolf

Fractional Calculus and Applied Analysis (2007)

- Volume: 10, Issue: 3, page 269-308
- ISSN: 1311-0454

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topMainardi, 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 -

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