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Theory and applications of fractional differential equations

紀錄類型:	書目-電子資源 : 單行本
正題名/作者:	Theory and applications of fractional differential equations/ Anatoly A. Kilbas, Hari M. Srivastava, Juan J. Trujillo.
作者:	Kilbas, A. A.
其他作者:	Srivastava, H. M.
出版者:	Amsterdam ;Elsevier, : 2006.,
面頁冊數:	xv, 523 p. :ill. ; : 25 cm.;
叢書名:	North-Holland mathematics studies ;
標題:	Fractional calculus. -
電子資源:	An electronic book accessible through the World Wide Web; click for information
ISBN:	9780444518323

Theory and applications of fractional differential equations
Kilbas, A. A.

Theory and applications of fractional differential equations[electronic resource] /Anatoly A. Kilbas, Hari M. Srivastava, Juan J. Trujillo. - 1st ed. - Amsterdam ;Elsevier,2006. - xv, 523 p. :ill. ;25 cm. - North-Holland mathematics studies ;204.

Includes bibliographical references (p. 469-520) and index.

1. Preliminaries. -- 2. Fractional Integrals and Fractional Derivatives. -- 3. Ordinary Fractional Differential Equations. Existence and Uniqueness Theorems. -- 4. Methods for Explicitly solving Fractional Differential Equations. -- 5. Integral Transform Methods for Explicit Solutions to Fractional Differential Equations. -- 6. Partial Fractional Differential Equations. -- 7. Sequential Linear Differential Equations of Fractional Order. -- 8. Further Applications of Fractional Models. -- Bibliography -- Subject Index.

This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. The subject of fractional calculus and its applications (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. Some of the areas of present-day applications of fractional models include Fluid Flow, Solute Transport or Dynamical Processes in Self-Similar and Porous Structures, Diffusive Transport akin to Diffusion, Material Viscoelastic Theory, Electromagnetic Theory, Dynamics of Earthquakes, Control Theory of Dynamical Systems, Optics and Signal Processing, Bio-Sciences, Economics, Geology, Astrophysics, Probability and Statistics, Chemical Physics, and so on. In the above-mentioned areas, there are phenomena with estrange kinetics which have a microscopic complex behaviour, and their macroscopic dynamics can not be characterized by classical derivative models. The fractional modelling is an emergent tool which use fractional differential equations including derivatives of fractional order, that is, we can speak about a derivative of order 1/3, or square root of 2, and so on. Some of such fractional models can have solutions which are non-differentiable but continuous functions, such as Weierstrass type functions. Such kinds of properties are, obviously, impossible for the ordinary models. What are the useful properties of these fractional operators which help in the modelling of so many anomalous processes? From the point of view of the authors and from known experimental results, most of the processes associated with complex systems have non-local dynamics involving long-memory in time, and the fractional integral and fractional derivative operators do have some of those characteristics. This book is written primarily for the graduate students and researchers in many different disciplines in the mathematical, physical, engineering and so many others sciences, who are interested not only in learning about the various mathematical tools and techniques used in the theory and widespread applications of fractional differential equations, but also in further investigations which emerge naturally from (or which are motivated substantially by) the physical situations modelled mathematically in the book. This monograph consists of a total of eight chapters and a very extensive bibliography. The main objective of it is to complement the contents of the other books dedicated to the study and the applications of fractional differential equations. The aim of the book is to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy type problems involving nonlinear ordinary fractional differential equations, explicit solutions of linear differential equations and of the corresponding initial-value problems through different methods, closed-form solutions of ordinary and partial differential equations, and a theory of the so-called sequential linear fractional differential equations including a generalization of the classical Frobenius method, and also to include an interesting set of applications of the developed theory. Key features: - It is mainly application oriented. - It contains a complete theory of Fractional Differential Equations. - It can be used as a postgraduate-level textbook in many different disciplines within science and engineering. - It contains an up-to-date bibliography. - It provides problems and directions for further investigations. - Fractional Modelling is an emergent tool with demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. - It contains many examples. - and so on!

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780444518323

Source: 130372:130475Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

121263
Fractional calculus.
Index Terms--Genre/Form:

96803
Electronic books.

LC Class. No.: QA314 / .K55 2006eb

Dewey Class. No.: 515/.83

Theory and applications of fractional differential equations
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300 $a xv, 523 p. : $b ill. ; $c 25 cm.
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504 $a Includes bibliographical references (p. 469-520) and index.
505 0 $a 1. Preliminaries. -- 2. Fractional Integrals and Fractional Derivatives. -- 3. Ordinary Fractional Differential Equations. Existence and Uniqueness Theorems. -- 4. Methods for Explicitly solving Fractional Differential Equations. -- 5. Integral Transform Methods for Explicit Solutions to Fractional Differential Equations. -- 6. Partial Fractional Differential Equations. -- 7. Sequential Linear Differential Equations of Fractional Order. -- 8. Further Applications of Fractional Models. -- Bibliography -- Subject Index.
520 $a This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. The subject of fractional calculus and its applications (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. Some of the areas of present-day applications of fractional models include Fluid Flow, Solute Transport or Dynamical Processes in Self-Similar and Porous Structures, Diffusive Transport akin to Diffusion, Material Viscoelastic Theory, Electromagnetic Theory, Dynamics of Earthquakes, Control Theory of Dynamical Systems, Optics and Signal Processing, Bio-Sciences, Economics, Geology, Astrophysics, Probability and Statistics, Chemical Physics, and so on. In the above-mentioned areas, there are phenomena with estrange kinetics which have a microscopic complex behaviour, and their macroscopic dynamics can not be characterized by classical derivative models. The fractional modelling is an emergent tool which use fractional differential equations including derivatives of fractional order, that is, we can speak about a derivative of order 1/3, or square root of 2, and so on. Some of such fractional models can have solutions which are non-differentiable but continuous functions, such as Weierstrass type functions. Such kinds of properties are, obviously, impossible for the ordinary models. What are the useful properties of these fractional operators which help in the modelling of so many anomalous processes? From the point of view of the authors and from known experimental results, most of the processes associated with complex systems have non-local dynamics involving long-memory in time, and the fractional integral and fractional derivative operators do have some of those characteristics. This book is written primarily for the graduate students and researchers in many different disciplines in the mathematical, physical, engineering and so many others sciences, who are interested not only in learning about the various mathematical tools and techniques used in the theory and widespread applications of fractional differential equations, but also in further investigations which emerge naturally from (or which are motivated substantially by) the physical situations modelled mathematically in the book. This monograph consists of a total of eight chapters and a very extensive bibliography. The main objective of it is to complement the contents of the other books dedicated to the study and the applications of fractional differential equations. The aim of the book is to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy type problems involving nonlinear ordinary fractional differential equations, explicit solutions of linear differential equations and of the corresponding initial-value problems through different methods, closed-form solutions of ordinary and partial differential equations, and a theory of the so-called sequential linear fractional differential equations including a generalization of the classical Frobenius method, and also to include an interesting set of applications of the developed theory. Key features: - It is mainly application oriented. - It contains a complete theory of Fractional Differential Equations. - It can be used as a postgraduate-level textbook in many different disciplines within science and engineering. - It contains an up-to-date bibliography. - It provides problems and directions for further investigations. - Fractional Modelling is an emergent tool with demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. - It contains many examples. - and so on!
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