Download or read book Advanced Applications of Fractional Differential Operators to Science and Technology written by Matouk, Ahmed Ezzat and published by IGI Global. This book was released on 2020-04-24 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional-order calculus dates to the 19th century but has been resurrected as a prevalent research subject due to its provision of more adequate and realistic descriptions of physical aspects within the science and engineering fields. What was once a classical form of mathematics is currently being reintroduced as a new modeling technique that engineers and scientists are finding modern uses for. There is a need for research on all facets of these fractional-order systems and studies of its potential applications. Advanced Applications of Fractional Differential Operators to Science and Technology provides emerging research exploring the theoretical and practical aspects of novel fractional modeling and related dynamical behaviors as well as its applications within the fields of physical sciences and engineering. Featuring coverage on a broad range of topics such as chaotic dynamics, ecological models, and bifurcation control, this book is ideally designed for engineering professionals, mathematicians, physicists, analysts, researchers, educators, and students seeking current research on fractional calculus and other applied mathematical modeling techniques.

Download or read book Theory and Applications of Fractional Differential Equations written by A.A. Kilbas and published by Elsevier. This book was released on 2006-02-16 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.

Download or read book Fractional Calculus written by Roy Abi Zeid Daou and published by Nova Science Publishers. This book was released on 2014-01-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of this two-volume book, presents history, the mathematical modelling and the applications of fractional order systems, and contains mathematical and theoretical studies and research related to this domain. This volume is made up of 11 chapters. The first chapter presents an analysis of the Caputo derivative and the pseudo state representation with the infinite state approach. The second chapter studies the stability of a class of fractional Cauchy problems. The third chapter shows how to solve fractional order differential equations and fractional order partial differential equations using modern matrix algebraic approaches. Following this chapter, chapter four proposes another analytical method to solve differential equations with local fractional derivative operators. Concerning chapter five, it presents the extended Borel transform and its related fractional analysis. After presenting the analytical resolution methods for fractional calculus, chapter six shows the essentials of fractional calculus on discrete settings. The initialisation of such systems is shown in chapter seven. In fact, this chapter presents a generalised application of the Hankel operator for initialisation of fractional order systems. The last four chapters show some new studies and applications of non-integer calculus. In fact, chapter eight presents the fractional reaction-transport equations and evanescent continuous time random walks. Chapter nine shows a novel approach in the exponential integrators for fractional differential equations. Chapter ten presents the non-fragile tuning of fractional order PD controllers for integrating time delay systems. At the end, chapter eleven proposes a discrete finite-dimensional approximation of linear infinite dimensional systems. To sum up, this volume presents a mathematical and theoretical study of fractional calculus along with a stability study and some applications. This volume ends up with some new techniques and methods applied in fractional calculus. This volume will be followed up by a second volume that focuses on the applications of fractional calculus in several engineering domains.

Download or read book General Fractional Derivatives written by Xiao-Jun Yang and published by CRC Press. This book was released on 2019-05-10 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.

Download or read book Research Advancements in Smart Technology Optimization and Renewable Energy written by Vasant, Pandian and published by IGI Global. This book was released on 2020-08-07 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: As environmental issues remain at the forefront of energy research, renewable energy is now an all-important field of study. And as smart technology continues to grow and be refined, its applications broaden and increase in their potential to revolutionize sustainability studies. This potential can only be fully realized with a thorough understanding of the most recent breakthroughs in the field. Research Advancements in Smart Technology, Optimization, and Renewable Energy is a collection of innovative research that explores the recent steps forward for smart applications in sustainability. Featuring coverage on a wide range of topics including energy assessment, neural fuzzy control, and biogeography, this book is ideally designed for advocates, policymakers, engineers, software developers, academicians, researchers, and students.

Download or read book Handbook of Research on Engineering Innovations and Technology Management in Organizations written by Gaur, Loveleen and published by IGI Global. This book was released on 2020-04-17 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: As technology weaves itself more tightly into everyday life, socio-economic development has become intricately tied to these ever-evolving innovations. Technology management is now an integral element of sound business practices, and this revolution has opened up many opportunities for global communication. However, such swift change warrants greater research that can foresee and possibly prevent future complications within and between organizations. The Handbook of Research on Engineering Innovations and Technology Management in Organizations is a collection of innovative research that explores global concerns in the applications of technology to business and the explosive growth that resulted. Highlighting a wide range of topics such as cyber security, legal practice, and artificial intelligence, this book is ideally designed for engineers, manufacturers, technology managers, technology developers, IT specialists, productivity consultants, executives, lawyers, programmers, managers, policymakers, academicians, researchers, and students.

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.

Download or read book Industrial Internet of Things and Cyber Physical Systems Transforming the Conventional to Digital written by Kumar, Pardeep and published by IGI Global. This book was released on 2020-05-22 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the help of artificial intelligence, machine learning, and big data analytics, the internet of things (IoT) is creating partnerships within industry where machines, processes, and humans communicate with one another. As this radically changes traditional industrial operations, this results in the rapid design, cheap manufacture, and effective customization of products. Answering the growing demand of customers and their preferences has become a challenge for such partnerships. Industrial Internet of Things and Cyber-Physical Systems: Transforming the Conventional to Digital is a collection of innovative research that discusses development, implementation, and business impacts of IoT technologies on sustainable societal development and improved life quality. Highlighting a wide range of topics such as green technologies, wireless networks, and IoT policy, this book is ideally designed for technology developers, entrepreneurs, industrialists, programmers, engineers, technicians, researchers, academicians, and students.

Download or read book Strategies to Overcome Superbug Invasions Emerging Research and Opportunities written by Chopra, Dimple Sethi and published by IGI Global. This book was released on 2021-06-25 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, there has been an upsurge in microbial infections. Extensive and inappropriate usage of antimicrobial drugs in treating infections has led to the evolution of a resistant strain of microorganisms and irreversible immunosuppression in humans. Medical institutions and hospitals require solutions to combat these contagions in order to avoid future epidemics. Strategies to Overcome Superbug Invasions: Emerging Research and Opportunities highlights current research and potential strategies to prevent the emergence and re-emergence of drug-resistant pathogenic microbial strains. The content within this publication examines biosensing, global initiatives, nanomaterials, and alternative therapies. It is designed for microbiologists, biotechnologists, pharmacists, pharmacologists, virologists, formulation scientists, infectious disease specialists, government officials, policymakers, healthcare practitioners, doctors, nurses, hospital directors, researchers, surgeons, and academicians who are seeking research on innovative solutions for multi-drug-resistant infections.

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.

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.

Download or read book Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics written by Elina Shishkina and published by Academic Press. This book was released on 2020-07-24 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights.

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

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:

Download or read book Advanced Numerical Methods for Differential Equations written by Harendra Singh and published by CRC Press. This book was released on 2021-06-25 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

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

Download or read book Computational Fractional Dynamical Systems written by Snehashish Chakraverty and published by John Wiley & Sons. This book was released on 2022-11-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous presentation of different expansion and semi-analytical methods for fractional differential equations Fractional differential equations, differential and integral operators with non-integral powers, are used in various science and engineering applications. Over the past several decades, the popularity of the fractional derivative has increased significantly in diverse areas such as electromagnetics, financial mathematics, image processing, and materials science. Obtaining analytical and numerical solutions of nonlinear partial differential equations of fractional order can be challenging and involve the development and use of different methods of solution. Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications presents a variety of computationally efficient semi-analytical and expansion methods to solve different types of fractional models. Rather than focusing on a single computational method, this comprehensive volume brings together more than 25 methods for solving an array of fractional-order models. The authors employ a rigorous and systematic approach for addressing various physical problems in science and engineering. Covers various aspects of efficient methods regarding fractional-order systems Presents different numerical methods with detailed steps to handle basic and advanced equations in science and engineering Provides a systematic approach for handling fractional-order models arising in science and engineering Incorporates a wide range of methods with corresponding results and validation Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications is an invaluable resource for advanced undergraduate students, graduate students, postdoctoral researchers, university faculty, and other researchers and practitioners working with fractional and integer order differential equations.