Lie Symmetry Analysis Of Fractional Differential Equations
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| Author | : Mir Sajjad Hashemi |
| Publisher | : CRC Press |
| Total Pages | : 223 |
| Release | : 2020-07-09 |
| Genre | : Mathematics |
| ISBN | : 1000068935 |
The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications. It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications. In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here. The book also includes generalization of Lie symmetries for fractional integro differential equations. Features Provides a solid basis for understanding fractional calculus, before going on to explore in detail Lie Symmetries and their applications Useful for PhD and postdoc graduates, as well as for all mathematicians and applied researchers who use the powerful concept of Lie symmetries Filled with various examples to aid understanding of the topics
| Author | : Nailʹ Khaĭrullovich Ibragimov |
| Publisher | : John Wiley & Sons |
| Total Pages | : 376 |
| Release | : 1999-05-04 |
| Genre | : Mathematics |
| ISBN | : |
Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. * This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory * Includes a concise and self contained introduction to differential equations * Easy to follow and comprehensive introduction to Lie group analysis * The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.
| Author | : Anatoly Kochubei |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 528 |
| Release | : 2019-02-19 |
| Genre | : Mathematics |
| ISBN | : 3110571668 |
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 second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
| Author | : Daniel J. Arrigo |
| Publisher | : John Wiley & Sons |
| Total Pages | : 190 |
| Release | : 2015-01-20 |
| Genre | : Mathematics |
| ISBN | : 1118721403 |
A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. Thoroughly class-tested, the author presents classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. Symmetry Analysis of Differential Equations: An Introduction also features: Detailed, step-by-step examples to guide readers through the methods of symmetry analysis End-of-chapter exercises, varying from elementary to advanced, with select solutions to aid in the calculation of the presented algorithmic methods Symmetry Analysis of Differential Equations: An Introduction is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics. The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations.
| Author | : Peter Ellsworth Hydon |
| Publisher | : Cambridge University Press |
| Total Pages | : 230 |
| Release | : 2000-01-28 |
| Genre | : Mathematics |
| ISBN | : 9780521497862 |
This book is a straightforward introduction to the subject of symmetry methods for solving differential equations, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily.The book contains some methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.
| Author | : Peter J. Olver |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 524 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468402749 |
This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.
| Author | : Phool Singh |
| Publisher | : Springer Nature |
| Total Pages | : 372 |
| Release | : 2020-09-30 |
| Genre | : Technology & Engineering |
| ISBN | : 9811554145 |
This book presents various computational and cognitive modeling approaches in the areas of health, education, finance, theenvironment, engineering, commerce and industry. Gathering selected conference papers presented atthe International Conference on Trends in Computational and Cognitive Engineering (TCCE), it sharescutting-edge insights and ideas from mathematicians, engineers, scientists and researchers anddiscusses fresh perspectives on problem solving in a range of research areas.
| Author | : L. V. Ovsiannikov |
| Publisher | : Academic Press |
| Total Pages | : 433 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483219062 |
Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.
| Author | : George W. Bluman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 424 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475743076 |
A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag, 1974, by the first author and J.D. Cole. The present book also includes a thorough and comprehensive treatment of Lie groups of tranformations and their various uses for solving ordinary and partial differential equations. No knowledge of group theory is assumed. Emphasis is placed on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This book should be particularly suitable for physicists, applied mathematicians, and engineers. Almost all of the examples are taken from physical and engineering problems including those concerned with heat conduction, wave propagation, and fluid flows. A preliminary version was used as lecture notes for a two-semester course taught by the first author at the University of British Columbia in 1987-88 to graduate and senior undergraduate students in applied mathematics and physics. Chapters 1 to 4 encompass basic material. More specialized topics are covered in Chapters 5 to 7.
| Author | : Nail H Ibragimov |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 365 |
| Release | : 2009-11-19 |
| Genre | : Mathematics |
| ISBN | : 9813107766 |
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book — which aims to present new mathematical curricula based on symmetry and invariance principles — is tailored to develop analytic skills and “working knowledge” in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author's extensive teaching experience at Novosibirsk and Moscow universities in Russia, Collège de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.
