Fractional Calculus

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

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.

More Books:

Fractional Calculus
Language: en
Pages: 476
Authors: Dumitru Baleanu, Kai Diethelm, Enrico Scalas, Juan J Trujillo
Categories: Mathematics
Type: BOOK - Published: 2016-09-15 - Publisher: World Scientific

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,
Fractional Calculus
Language: en
Pages: 400
Authors: Dumitru Baleanu, Kai Diethelm, Enrico Scalas
Categories: Mathematics
Type: BOOK - Published: 2012 - Publisher: World Scientific

This title 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.
Discontinuity and Complexity in Nonlinear Physical Systems
Language: en
Pages: 433
Authors: J. A. Tenreiro Machado, Dumitru Baleanu, Albert C J Luo
Categories: Technology & Engineering
Type: BOOK - Published: 2013-12-04 - Publisher: Springer Science & Business Media

Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to
Fractional Calculus: Models And Numerical Methods
Language: en
Pages: 428
Authors: Baleanu Dumitru, Diethelm Kai, Scalas Enrico
Categories: Mathematics
Type: BOOK - Published: 2012-01-27 - Publisher: World Scientific

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
Basic Theory
Language: en
Pages: 489
Authors: Anatoly Kochubei, Yuri Luchko
Categories: Mathematics
Type: BOOK - Published: 2019-02-19 - Publisher: Walter de Gruyter GmbH & Co KG

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other