Fractional Calculus: Models and Numerical Methods - Couverture rigide

Baleanu, Dumitru; Diethelm, Kai; Scalas, Enrico; Trujillo, Juan J

 
9789814355209: Fractional Calculus: Models and Numerical Methods
Couverture rigide
ISBN 10 : 9814355208 ISBN 13 : 9789814355209
Editeur : World Scientific Publishing Co Pte Ltd, 2012

Synopsis

The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.

This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.

All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided. Contents: Preliminaries; A Survey of Numerical Methods for the Solution of Ordinary and Partial Fractional Differential Equations; Efficient Numerical Methods; Generalized Stirling Numbers and Applications; Fractional Variational Principles; CTRW and Fractional Diffusion Models; Applications of CTRW to Finance and Economics;

Readership: Undergraduate and graduate students, researchers and professionals in applied mathematics, analysis & differential equations and probability & statistics.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.

This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.

All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided. Contents: Preliminaries; A Survey of Numerical Methods for the Solution of Ordinary and Partial Fractional Differential Equations; Efficient Numerical Methods; Generalized Stirling Numbers and Applications; Fractional Variational Principles; CTRW and Fractional Diffusion Models; Applications of CTRW to Finance and Economics;

Readership: Undergraduate and graduate students, researchers and professionals in applied mathematics, analysis & differential equations and probability & statistics.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
World Scientific Publishing Co Pte Ltd
Date d'édition
2012
Langue
anglais
ISBN 10 
9814355208
ISBN 13 
9789814355209
Reliure
Relié
Nombre de pages
428
Coordonnées du fabricant
non disponible
Personne responsable
gpsr@libri.de
gpsr@libri.de

Friedensallee 273
Hamburg
22763
Allemagne