Diethelm Kai's Books

The Analysis of Fractional Differential Equations

An Application-Oriented Exposition Using Differential Operators of Caputo Type

By: Kai Diethelm

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The Analysis of Fractional Differential Equations

An Application-Oriented Exposition Using Differential Operators of Caputo Type

By: Kai Diethelm

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

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Page Count

251

Publisher

Springer

Published Date

ISBN 10

3642145744

ISBN 13

9783642145742

The Analysis of Fractional Differential Equations

An Application-Oriented Exposition Using Differential Operators of Caputo Type

By: Kai Diethelm

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The Analysis of Fractional Differential Equations

An Application-Oriented Exposition Using Differential Operators of Caputo Type

By: Kai Diethelm

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Page Count

251

Publisher

Springer

Published Date

ISBN 10

3642145744

ISBN 13

9783642145742

Fractional Calculus: Models And Numerical Methods

By: Dumitru Baleanu,Kai Diethelm,Enrico Scalas,Juan J Trujillo

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Fractional Calculus: Models And Numerical Methods

By: Dumitru Baleanu,Kai Diethelm,Enrico Scalas,Juan J Trujillo

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.

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Page Count

426

Publisher

World Scientific

Published Date

ISBN 10

9814458635

ISBN 13

9789814458634

Fractional Calculus: Models And Numerical Methods (Second Edition)

By: Juan J Trujillo,Enrico Scalas,Kai Diethelm,Dumitru Baleanu

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Fractional Calculus: Models And Numerical Methods (Second Edition)

By: Juan J Trujillo,Enrico Scalas,Kai Diethelm,Dumitru Baleanu

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 will keep in mind the trade-off 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.The second edition of the book has been expanded and now includes a discussion of additional, newly developed numerical methods for fractional calculus and a chapter on the application of fractional calculus for modeling processes in the life sciences.

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Page Count

477

Publisher

World Scientific

Published Date

ISBN 10

9813140054

ISBN 13

9789813140059

Fractional Calculus: Models And Numerical Methods (Second Edition)

By: Juan J Trujillo,Enrico Scalas,Kai Diethelm,Dumitru Baleanu

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Fractional Calculus: Models And Numerical Methods (Second Edition)

By: Juan J Trujillo,Enrico Scalas,Kai Diethelm,Dumitru Baleanu

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Solve jigsaw puzzle

Age

Page Count

477

Publisher

World Scientific

Published Date

ISBN 10

9813140054

ISBN 13

9789813140059

Fractional Calculus

Models and Numerical Methods

By: Dumitru Baleanu,Juan J. Trujillo

Write a review Read reviews Take a Quiz Solve Book Puzzle

Fractional Calculus

Models and Numerical Methods

By: Dumitru Baleanu,Juan J. Trujillo

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 will keep in mind the trade-off 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. The second edition of the book has been expanded and now includes a discussion of additional, newly developed numerical methods for fractional calculus and a chapter on the application of fractional calculus for modeling processes in the life sciences.

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Page Count

448

Publisher

Series on Complexity, Nonlinearity, and Chaos

Published Date

ISBN 10

9813140038

ISBN 13

9789813140035

Book's by Diethelm Kai

The Analysis of Fractional Differential Equations

The Analysis of Fractional Differential Equations

The Analysis of Fractional Differential Equations

The Analysis of Fractional Differential Equations

Fractional Calculus: Models And Numerical Methods

Fractional Calculus: Models And Numerical Methods

Fractional Calculus: Models And Numerical Methods (Second Edition)

Fractional Calculus: Models And Numerical Methods (Second Edition)

Fractional Calculus: Models And Numerical Methods (Second Edition)

Fractional Calculus: Models And Numerical Methods (Second Edition)

Fractional Calculus

Fractional Calculus

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