Fractional calculus : models and numerical methods
 Language
 English.
 Imprint
 Singapore ; Hackensack, NJ : World Scientific, c2012.
 Physical description
 xxiv, 400 p. : ill ; 24 cm.
 Series
 Series on complexity, nonlinearity and chaos ; v. 3.
Access
Available online
 www.worldscientific.com World Scientific
 ebrary

Stacks

Unknown
QA314 .F74 2012

Unknown
QA314 .F74 2012
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Contributors
 Contributor
 Baleanu, D. (Dumitru)
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 363395) and index.
 Contents

 Survey of Numerical Methods to Solve Ordinary and Partial Fractional Differential Equations Specific and Efficient Methods to Solve Ordinary and Partial Fractional Differential Equations Fractional Variational Principles ContinuousTime Random Walks (CTRWs) Applications to Finance and Economics Generalized Stirling Numbers of First and Second Kind in the Framework of Fractional Calculus.
 (source: Nielsen Book Data)
 Publisher's Summary
 The subject of fractional calculus and its applications (that is, convolutiontype pseudodifferential 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 semiMarkov continuoustime random walks and the spacetime fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tickbytick (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 currently existing in the market. This book will be written with a tradeoff 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Fractional calculus.
Bibliographic information
 Publication date
 2012
 Responsibility
 Dumitru Baleanu ... [et al.].
 Series
 CNC Series on complexity, nonlinearity, and chaos ; v. 3
 ISBN
 9789814355209
 9814355208