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# Fractional calculus: models and numerical methods (2nd edition)

book

posted on 2023-06-09, 03:55 authored by Dumitru Baleanu, Kai Diethelm, Enrico Scalas, Juan J TrujilloThis 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. Contents: Preface Preface to the Second Edition Preliminaries A Survey of Numerical Methods for the Solution of Ordinary and Partial Fractional Differential Equations Specific Efficient Methods for the Solution of Ordinary and Partial Fractional Differential Equations Generalized Stirling Numbers and Applications Fractional Variational Principles Continuous-Time Random Walks and Fractional Diffusion Models Applications of Continuous-Time Random Walks Selected Applications of Fractional Calculus Models in the Life Sciences Appendix: Source Codes Bibliography Index Readership: Undergraduate and graduate students in mathematics as well as researchers in applied mathematics and applied sciences whose interests involve differential equations, fractional calculus, special functions, variational methods, numerical methods and their applications in physics, mechanics, engineering, finance, economics and other applied fields including life science and social science.

## History

## Publication status

- Published

## Publisher

World Scientific## Volume

5## Pages

476.0## Place of publication

Singapore## ISBN

9789813140035## Series

Series on complexity, nonlinearity and chaos## Department affiliated with

- Mathematics Publications

## Research groups affiliated with

- Probability and Statistics Research Group Publications

## Full text available

- No

## Peer reviewed?

- Yes

## Legacy Posted Date

2016-11-07## Usage metrics

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