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Recent Trends In Fractional Calculus And Its Applications
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Book Synopsis Recent Trends in Fractional Calculus and Its Applications by : Praveen Agarwal
Download or read book Recent Trends in Fractional Calculus and Its Applications written by Praveen Agarwal and published by Elsevier. This book was released on 2024-07-02 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics.The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences. - Provides the most recent and up-to-date developments in the Fractional Calculus and its application areas - Presents pre-preparation ideas to help researchers/scientists/clinicians face the new challenges in the application of fractional differential equations - Helps researchers and scientists understand the importance of the Fractional Calculus to solve many problems in Biomedical Engineering and applied sciences
Book Synopsis New Trends in Nanotechnology and Fractional Calculus Applications by : Dumitru Baleanu
Download or read book New Trends in Nanotechnology and Fractional Calculus Applications written by Dumitru Baleanu and published by Springer Science & Business Media. This book was released on 2010-03-14 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians.
Book Synopsis Fractional Calculus and Its Applications by : B. Ross
Download or read book Fractional Calculus and Its Applications written by B. Ross and published by Springer. This book was released on 2006-11-15 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Trends in Fractional Differential Equations with Real-World Applications in Physics by : Jagdev Singh
Download or read book New Trends in Fractional Differential Equations with Real-World Applications in Physics written by Jagdev Singh and published by Frontiers Media SA. This book was released on 2020-12-30 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractional Calculus with its Applications in Engineering and Technology by : Yi Yang
Download or read book Fractional Calculus with its Applications in Engineering and Technology written by Yi Yang and published by Springer Nature. This book was released on 2022-05-31 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Fractional Order Analysis by : Hemen Dutta
Download or read book Fractional Order Analysis written by Hemen Dutta and published by John Wiley & Sons. This book was released on 2020-09-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
Book Synopsis Fractional Calculus and Fractional Differential Equations by : Varsha Daftardar-Gejji
Download or read book Fractional Calculus and Fractional Differential Equations written by Varsha Daftardar-Gejji and published by Springer. This book was released on 2019-08-10 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed. The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.
Book Synopsis Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering by : Praveen Agarwal
Download or read book Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering written by Praveen Agarwal and published by Bentham Science Publishers. This book was released on 2023-04-11 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, special functions have been developed and applied in a variety of fields, such as combinatorics, astronomy, applied mathematics, physics, and engineering due to their remarkable properties. This volume expands our understanding of special functions by highlighting recent trends in numerical analysis. Interesting applications of special functions and partial differential equations are demonstrated by 15 chapters. Many chapters highlight the importance of numerical techniques and the results of complex analysis. Contributions in the book emphasize the mathematical treatment of questions arising in natural sciences and engineering, particularly those that involve novel problems and their solutions. This volume is a timely update for mathematicians and researchers interested in advanced numerical methods and computational techniques used to solve complex problems List of Chapters 1. Modified Adaptive Synchronization and Anti Synchronization method for Fractional order chaotic systems with uncertain parameters 2. Improved generalized differential transform method for a class of linear non homogeneous ordinary fractional differential equation 3. Incomplete K2-Function 4. Some Results On Incomplete Hypergeometric Functions 5. Transcendental Bernstein Series: Interpolation and Approximation 6. Some Sufficient Conditions For Uniform Convexity Of Normalized 1F2 Function 7. From Abel continuity theorem to Paley-Wiener theorem… 8. A New Class of Truncated Exponential-Gould-Hopper basedGenocchi Polynomials 9. Computational preconditioned Gauss-Seidel via half-sweep approximation to Caputo's time fractional differential equations 10. Krasnoselskii-type Theorems for Monotone Operators in Ordered Banach Algebra with Applications in Fractional Differential Equations and Inclusion 11. General fractional order quadratic functional integral equations: Existence, properties of solutions and some of its Applications 12.Nonlinear set-valued delay functional integral equations of Volterra-Stieltjes type: Existence of solutions, continuous dependence and applications 13.Certain Saigo Fractional Derivatives Of Extended Hypergeometric Functions 14. Some Erdelyi-kober Fractional Integrals Of The Extended Hypergeometric Functions 15. On solutions of Kinetic Model by Sumudu transform
Book Synopsis Fractional Calculus: New Applications in Understanding Nonlinear Phenomena by : Mehmet Yavuz
Download or read book Fractional Calculus: New Applications in Understanding Nonlinear Phenomena written by Mehmet Yavuz and published by Bentham Science Publishers. This book was released on 2022-12-14 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractional Differential Equations by : Anatoly Kochubei
Download or read book Fractional Differential Equations written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applications Of Fractional Calculus In Physics by : Rudolf Hilfer
Download or read book Applications Of Fractional Calculus In Physics written by Rudolf Hilfer and published by World Scientific. This book was released on 2000-03-02 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances in Non-Integer Order Calculus and Its Applications by : Agnieszka B. Malinowska
Download or read book Advances in Non-Integer Order Calculus and Its Applications written by Agnieszka B. Malinowska and published by Springer. This book was released on 2019-04-17 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of some recent findings in the theory and applications of non-integer order systems. Discussing topics ranging from the mathematical foundations to technical applications of continuous-time and discrete-time fractional calculus, it includes 22 original research papers and is subdivided into four parts: • Mathematical Foundations • Approximation, Modeling and Simulations • Fractional Systems Analysis and Control • Applications The papers were selected from those presented at the 10th International Conference of Non-integer Order Calculus and its Applications, which was held at the Bialystok University of Technology, Poland, September 20–21, 2018. Thanks to the broad spectrum of topics covered, the book is suitable for researchers from applied mathematics and engineering. It is also a valuable resource for graduate students, as well as for scholars looking for new mathematical tools.
Book Synopsis Fractional Derivatives with Mittag-Leffler Kernel by : José Francisco Gómez
Download or read book Fractional Derivatives with Mittag-Leffler Kernel written by José Francisco Gómez and published by Springer. This book was released on 2019-02-13 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractional Calculus by : Dumitru Baleanu
Download or read book Fractional Calculus written by Dumitru Baleanu and published by World Scientific. This book was released on 2012 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential 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 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 was written with a trade-off 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. Numerical code is also provided.
Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm
Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer. This book was released on 2010-08-18 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Book Synopsis Fractional Differential Equations by : Igor Podlubny
Download or read book Fractional Differential Equations written by Igor Podlubny and published by Elsevier. This book was released on 1998-10-27 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. - A unique survey of many applications of fractional calculus - Presents basic theory - Includes a unified presentation of selected classical results, which are important for applications - Provides many examples - Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory - The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches - Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives
Book Synopsis Non-Integer Order Calculus and its Applications by : Piotr Ostalczyk
Download or read book Non-Integer Order Calculus and its Applications written by Piotr Ostalczyk and published by Springer. This book was released on 2018-03-22 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on fractional calculus, presenting novel advances in both the theory and applications of non-integer order systems. At the end of the twentieth century it was predicted that it would be the calculus of the twenty-first century, and that prophecy is confirmed year after year. Now this mathematical tool is successfully used in a variety of research areas, like engineering (e.g. electrical, mechanical, chemical), dynamical systems modeling, analysis and synthesis (e.g technical, biological, economical) as well as in multidisciplinary areas (e.g. biochemistry, electrochemistry).As well as the mathematical foundations the book concentrates on the technical applications of continuous-time and discrete-time fractional calculus, investigating the identification, analysis and control of electrical circuits and dynamical systems. It also presents the latest results.Although some scientific centers and scientists are skeptical and actively criticize the applicability of fractional calculus, it is worth breaking through the scientific and technological walls. Because the “fractional community” is growing rapidly there is a pressing need for the exchange of scientific results. The book includes papers presented at the 9th International Conference on Non-integer Order Calculus and Its Applications and is divided into three parts:• Mathematical foundations• Fractional systems analysis and synthesis• System modelingSeven papers discuss the mathematical foundations, twelve papers address fractional order analysis and synthesis and three focus on dynamical system modeling by the fractional order differential and difference equations. It is a useful resource for fractional calculus scientific community.
