Frontiers In Fractional Calculus
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| Author | : Sachin Bhalekar |
| Publisher | : Bentham Science Publishers |
| Total Pages | : 381 |
| Release | : 2018-03-21 |
| Genre | : Mathematics |
| ISBN | : 1681085992 |
Download Frontiers in Fractional Calculus Book in PDF, Epub and Kindle
This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications. The information in the book is presented in four parts: 1. Fractional Diffusion Equations: (i) solutions of fractional diffusion equations using wavelet methods, (ii) the maximum principle for time fractional diffusion equations, (iii) nonlinear sub-diffusion equations. 2. Mathematical Analysis: (i) shifted Jacobi polynomials for solving and identifying coupled fractional delay differential equations, (ii) the monotone iteration principle in the theory of Hadamard fractional delay differential equations, (iii) dynamics of fractional order modified Bhalekar-Gejji System, (iv) Grunwald-Letnikov derivatives. 3. Computational Techniques: GPU computing of special mathematical functions used in fractional calculus. 4. Reviews: (i) the popular iterative method NIM, (ii) fractional derivative with non-singular kernels, (iii) some open problems in fractional order nonlinear system This is a useful reference for researchers and graduate level mathematics students seeking knowledge about of fractional calculus and applied mathematics.
| Author | : Dumitru Baleanu |
| Publisher | : Frontiers Media SA |
| Total Pages | : 93 |
| Release | : 2019-11-15 |
| Genre | : |
| ISBN | : 2889459586 |
Download Fractional Calculus and its Applications in Physics Book in PDF, Epub and Kindle
| Author | : George A Anastassiou |
| Publisher | : World Scientific |
| Total Pages | : 289 |
| Release | : 2015-08-06 |
| Genre | : Mathematics |
| ISBN | : 9814704458 |
Download Frontiers In Time Scales And Inequalities Book in PDF, Epub and Kindle
This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional calculus in the Caputo sense. Then, it shows representation formulae of functions on time scales and presents Ostrowski type inequalities, Landau type inequalities, Grüss type and comparison of means inequalities, all these over time scales. The volume continues with integral operator inequalities and their multivariate vectorial versions using convexity of functions, again all these over time scales. It follows the Grüss and Ostrowski type inequalities involving s-convexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite-Hadamard type inequalities using m-convexity and (s, m)-convexity. Finally, it introduces the reduction method in fractional calculus and its connection to fractional Ostrowski type inequalities is studied.This book's results are expected to find applications in many areas of pure and applied mathematics, especially in difference equations and fractional differential equations. The chapters are self-contained and can be read independently, and advanced courses can be taught out of it. It is suitable for researchers, graduate students, seminars of the above subjects, and serves well as an invaluable resource for all science libraries.
| Author | : Jagdev Singh |
| Publisher | : Frontiers Media SA |
| Total Pages | : 172 |
| Release | : 2020-12-30 |
| Genre | : Science |
| ISBN | : 2889663043 |
Download New Trends in Fractional Differential Equations with Real-World Applications in Physics Book in PDF, Epub and Kindle
This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.
| Author | : Delfim F M Torres |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 292 |
| Release | : 2012-09-14 |
| Genre | : Mathematics |
| ISBN | : 184816968X |
Download Introduction To The Fractional Calculus Of Variations Book in PDF, Epub and Kindle
This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler-Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV.The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature./a
| Author | : B. Ross |
| Publisher | : Springer |
| Total Pages | : 391 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540699759 |
Download Fractional Calculus and Its Applications Book in PDF, Epub and Kindle
| Author | : Rudolf Hilfer |
| Publisher | : World Scientific |
| Total Pages | : 473 |
| Release | : 2000-03-02 |
| Genre | : Science |
| ISBN | : 9814496200 |
Download Applications Of Fractional Calculus In Physics Book in PDF, Epub and Kindle
Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.
| Author | : Yi Yang |
| Publisher | : Springer Nature |
| Total Pages | : 95 |
| Release | : 2022-05-31 |
| Genre | : Technology & Engineering |
| ISBN | : 303179625X |
Download Fractional Calculus with its Applications in Engineering and Technology Book in PDF, Epub and Kindle
This book aims to provide the basic theory of fractional calculus and its applications based on practical schemes and approaches, illustrated with applicable engineering and technical examples, especially focusing on the fractional-order controller design. In the development of this book, the essential theorems and facts in the first two chapters are proven with rigorous mathematical analyses. In addition, the commonly used definitions of Grünwald-Letnikov, Riemann-Liouville, Caputo, and Miller-Ross fractional derivatives are introduced with their properties proved and linked to fractional-order controller design. The last chapter presents several enlightening scenarios of fractional-order control designs, for example, the suppression of machining chatter, the nonlinear motion control of a multilink robot, the simultaneous tracking and stabilization control of a rotary inverted pendulum, and the idle speed control of an internal combustion engine (ICE).
| Author | : José Francisco Gómez |
| Publisher | : Springer |
| Total Pages | : 341 |
| Release | : 2019-02-13 |
| Genre | : Technology & Engineering |
| ISBN | : 303011662X |
Download Fractional Derivatives with Mittag-Leffler Kernel Book in PDF, Epub and Kindle
This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.
| Author | : Mehmet Yavuz |
| Publisher | : Bentham Science Publishers |
| Total Pages | : 275 |
| Release | : 2022-12-14 |
| Genre | : Mathematics |
| ISBN | : 9815051946 |
Download Fractional Calculus: New Applications in Understanding Nonlinear Phenomena Book in PDF, Epub and Kindle
In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators.These have been intensively studied formodelling and analysing real-world phenomena. There is now a growing body of research on new methods to understand natural occurrences and tackle different problems. This book presents ten reviews of recent fractional operators split over three sections: 1. Chaotic Systems and Control (covers the Caputo fractional derivative, and a chaotic fractional-order financial system)2. Heat Conduction (covers the Duhamel theorem for time-dependent source terms, and the Cattaneo–Hristov model for oscillatory heat transfer)3. Computational Methods and Their Illustrative Applications (covers mathematical analysis for understanding 5 real-word phenomena: HTLV-1 infection of CD4+ T-cells, traveling waves, rumor-spreading, biochemical reactions, and the computational fluid dynamics of a non-powered floating object navigating in an approach channel) This volume is a resource for researchers in physics, biology, behavioral sciences, and mathematics who are interested in new applications of fractional calculus in the study of nonlinear phenomena.
