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New Trends In Nanotechnology And Fractional Calculus Applications
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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: 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 Discrete Fractional Calculus by : Piotr Ostalczyk
Download or read book Discrete Fractional Calculus written by Piotr Ostalczyk and published by World Scientific. This book was released on 2015-11-26 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing.
Book Synopsis Fractional Calculus in Medical and Health Science by : Devendra Kumar
Download or read book Fractional Calculus in Medical and Health Science written by Devendra Kumar and published by CRC Press. This book was released on 2020-07-09 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers applications of fractional calculus used for medical and health science. It offers a collection of research articles built into chapters on classical and modern dynamical systems formulated by fractional differential equations describing human diseases and how to control them. The mathematical results included in the book will be helpful to mathematicians and doctors by enabling them to explain real-life problems accurately. The book will also offer case studies of real-life situations with an emphasis on describing the mathematical results and showing how to apply the results to medical and health science, and at the same time highlighting modeling strategies. The book will be useful to graduate level students, educators and researchers interested in mathematics and medical science.
Book Synopsis Handbook of Fractional Calculus for Engineering and Science by : Harendra Singh
Download or read book Handbook of Fractional Calculus for Engineering and Science written by Harendra Singh and published by CRC Press. This book was released on 2022-02-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on. This Handbook: Provides reliable methods for solving fractional-order models in science and engineering. Contains efficient numerical methods and algorithms for engineering-related equations. Contains comparison of various methods for accuracy and validity. Demonstrates the applicability of fractional calculus in science and engineering. Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations. Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.
Book Synopsis Fractional Calculus by : Praveen Agarwal
Download or read book Fractional Calculus written by Praveen Agarwal and published by Springer Nature. This book was released on 2019-11-23 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects papers presented at the International Conference on Fractional Differentiation and its Applications (ICFDA), held at the University of Jordan, Amman, Jordan, on 16–18 July 2018. Organized into 13 chapters, the book discusses the latest trends in various fields of theoretical and applied fractional calculus. Besides an essential mathematical interest, its overall goal is a general improvement of the physical world models for the purpose of computer simulation, analysis, design and control in practical applications. It showcases the development of fractional calculus as an acceptable tool for a large number of diverse scientific communities due to more adequate modeling in various fields of mechanics, electricity, chemistry, biology, medicine, economics, control theory, as well as signal and image processing. The book will be a valuable resource for graduate students and researchers of mathematics and engineering.
Download or read book Basic Theory written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 489 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 first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.
Book Synopsis Fractional Calculus: Models And Numerical Methods by : Baleanu Dumitru
Download or read book Fractional Calculus: Models And Numerical Methods written by Baleanu Dumitru and published by World Scientific. This book was released on 2012-01-27 with total page 428 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 General Fractional Derivatives by : Xiao-Jun Yang
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 306 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.
Book Synopsis Fractional Order Signal Processing by : Saptarshi Das
Download or read book Fractional Order Signal Processing written by Saptarshi Das and published by Springer Science & Business Media. This book was released on 2011-09-15 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book tries to briefly introduce the diverse literatures in the field of fractional order signal processing which is becoming an emerging topic among an interdisciplinary community of researchers. This book is aimed at postgraduate and beginning level research scholars who would like to work in the field of Fractional Order Signal processing (FOSP). The readers should have preliminary knowledge about basic signal processing techniques. Prerequisite knowledge of fractional calculus is not essential and is exposited at relevant places in connection to the appropriate signal processing topics. Basic signal processing techniques like filtering, estimation, system identification, etc. in the light of fractional order calculus are presented along with relevant application areas. The readers can easily extend these concepts to varied disciplines like image or speech processing, pattern recognition, time series forecasting, financial data analysis and modeling, traffic modeling in communication channels, optics, biomedical signal processing, electrochemical applications and many more. Adequate references are provided in each category so that the researchers can delve deeper into each area and broaden their horizon of understanding. Available MATLAB tools to simulate FOSP theories are also introduced so that the readers can apply the theoretical concepts right-away and gain practical insight in the specific domain.
Book Synopsis Advances in the Theory and Applications of Non-integer Order Systems by : Wojciech Mitkowski
Download or read book Advances in the Theory and Applications of Non-integer Order Systems written by Wojciech Mitkowski and published by Springer Science & Business Media. This book was released on 2013-06-03 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents various aspects of non-integer order systems, also known as fractional systems, which have recently attracted an increasing attention in the scientific community of systems science, applied mathematics, control theory. Non-integer systems have become relevant for many fields of science and technology exemplified by the modeling of signal transmission, electric noise, dielectric polarization, heat transfer, electrochemical reactions, thermal processes, acoustics, etc. The content is divided into six parts, every of which considers one of the currently relevant problems. In the first part the Realization problem is discussed, with a special focus on positive systems. The second part considers stability of certain classes of non-integer order systems with and without delays. The third part is focused on such important aspects as controllability, observability and optimization especially in discrete time. The fourth part is focused on distributed systems where non-integer calculus leads to new and interesting results. The next part considers problems of solutions and approximations of non-integer order equations and systems. The final and most extensive part is devoted to applications. Problems from mechatronics, biomedical engineering, robotics and others are all analyzed and solved with tools from fractional systems. This volume came to fruition thanks to high level of talks and interesting discussions at RRNR 2013 - 5th Conference on Non-integer Order Calculus and its Applications that took place at AGH University of Science and Technology in Kraków, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.
Book Synopsis New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics by : Mustafa Inc
Download or read book New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics written by Mustafa Inc and published by Frontiers Media SA. This book was released on 2023-11-20 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various numerical and analytical methods have been used to investigate the models of real-world phenomena. Namely, real-world models from quantum physics have been investigated by many researchers. This Research Topic aims to promote and exchange new and important theoretical and numerical results to study the dynamics of complex physical systems. In particular, the Research Topic will focus on numerical and analytical methods for nonlinear partial differential equations which have applications for quantum physical systems. Authors are encouraged to introduce their latest original research articles. The Research Topic will cover, but is not limited to, the following themes: - Mathematical methods in physics - Representations of Lie groups in physics - Quantum fields - Advanced numerical methods and techniques for nonlinear partial differential equations - Schrödinger classical and fractional operators - Conservation laws
Book Synopsis Mathematical Economics by : Vasily E. Tarasov
Download or read book Mathematical Economics written by Vasily E. Tarasov and published by MDPI. This book was released on 2020-06-03 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.
Book Synopsis Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications by : Esteban Tlelo-Cuautle
Download or read book Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications written by Esteban Tlelo-Cuautle and published by Springer Nature. This book was released on 2019-11-11 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the simulation and optimization of integer and fractional-order chaotic systems, and how they can be implemented in the analog and digital domains using FPAAs and FPGAs. Design guidelines are provided to use commercially available electronic devices, and to perform hardware descriptions of integer/fractional-order chaotic systems programming in VHDL. Finally, several engineering applications oriented to cryptography, internet of things, robotics and chaotic communications, are detailed to highlight the usefulness of FPAA/FPGA based integer/fractional-order chaotic systems. Provides guidelines to implement fractional-order derivatives using commercially available devices; Describes details on using FPAAs to approach fractional-order chaotic systems; Includes details on using FPGAs to approach fractional-order chaotic systems, programming in VHDL and reducing hardware resources; Discusses applications to cryptography, internet of things, robotics and chaotic communications.
Book Synopsis Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems by : Boulkroune, Abdesselem
Download or read book Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems written by Boulkroune, Abdesselem and published by IGI Global. This book was released on 2018-05-11 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recent years, fractional-order systems have been studied by many researchers in the engineering field. It was found that many systems can be described more accurately by fractional differential equations than by integer-order models. Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems is a scholarly publication that explores new developments related to novel chaotic fractional-order systems, control schemes, and their applications. Featuring coverage on a wide range of topics including chaos synchronization, nonlinear control, and cryptography, this publication is geared toward engineers, IT professionals, researchers, and upper-level graduate students seeking current research on chaotic fractional-order systems and their applications in engineering and computer science.
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 229 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.
Book Synopsis Symmetry in Complex Systems by : J. A. Tenreiro Machado
Download or read book Symmetry in Complex Systems written by J. A. Tenreiro Machado and published by MDPI. This book was released on 2021-01-21 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex systems with symmetry arise in many fields, at various length scales, including financial markets, social, transportation, telecommunication and power grid networks, world and country economies, ecosystems, molecular dynamics, immunology, living organisms, computational systems, and celestial and continuum mechanics. The emergence of new orders and structures in complex systems means symmetry breaking and transitions from unstable to stable states. Modeling complexity has attracted many researchers from different areas, dealing both with theoretical concepts and practical applications. This Special Issue fills the gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems.
