Fractional Calculus New Applications In Understanding Nonlinear Phenomena
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Fractional Calculus New Applications In Understanding Nonlinear Phenomena
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Author : Mehmet Yavuz
language : en
Publisher: Bentham Science Publishers
Release Date : 2022-12-14
Fractional Calculus New Applications In Understanding Nonlinear Phenomena written by Mehmet Yavuz and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-14 with Mathematics categories.
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.
Fractional Dynamics In Natural Phenomena And Advanced Technologies
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Author : Dumitru Baleanu
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2024-01-29
Fractional Dynamics In Natural Phenomena And Advanced Technologies written by Dumitru Baleanu and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-29 with Juvenile Nonfiction categories.
This book addresses different applied problems in order to demonstrate the feasibility of fractional calculus’ use, irrespective of the type of memory kernels used, to model varieties of natural phenomena and new processes emerging in advanced technologies. In this context, the book’s focus is on modelling, adequate results, and interpretations, rather than theorems and proofs. The book includes a total of 12 chapters, representing various aspects of applied fractional modelling and covering important issues in modern technologies to provide a better understanding of applications of fractional calculus in applied modelling. The book will be a versatile source of information for undergraduate and graduate students, and for scientists involved in modelling of nonlinear and hereditary phenomena.
The Fundamentals Of Fractional Calculus
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Author : Dharmendra Kumar Singh
language : en
Publisher: CRC Press
Release Date : 2025-09-23
The Fundamentals Of Fractional Calculus written by Dharmendra Kumar Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-09-23 with Mathematics categories.
Fractional calculus is one of the most important divisions of theoretical and applied mathematics. This new book presents a wide variety of interesting technologies and practices used in fractional calculus, providing detailed insight into recent developments and the latest research in the field of science, engineering, etc., using fractional calculus. The result of the teaching experiences of the editors and authors to engineering and science students, the volume discusses fractional calculus via generalized functions and integral transforms of pathway type; Laplace transformation of fractional integrals and derivatives; estimating the order of derivation in a fractional differential equation; a new class of integro-differential equations with non-singular differential operators; various uses of the Caputo approach; a gingerbread-man discrete system; etc. The various applications of fractional calculus are shown with examples such as for creating and/or solving epidemic models, alcoholism models, model for divorce dynamics, and more. Giving a rigorous and thorough analysis of various aspects of fractional calculus, this volume helps scientific readers as well as researchers working in the area of fractional calculus to establish the key steps followed in the research methodology and concept development.
Advances In Mathematical Modelling Applied Analysis And Computation
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Author : Jagdev Singh
language : en
Publisher: Springer Nature
Release Date : 2023-04-12
Advances In Mathematical Modelling Applied Analysis And Computation written by Jagdev Singh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-12 with Technology & Engineering categories.
The book is very useful for researchers, graduate students and educators associated with or interested in recent advances in different aspects of modelling, computational methods and techniques necessary for solving problems arising in the real-world problems. The book includes carefully peer-reviewed research articles presented in the “5th International Conference on Mathematical Modelling, Applied Analysis and Computation”, held at JECRC University, Jaipur, during 4–6 August 2022 concentrating on current advances in mathematical modelling and computation via tools and techniques from mathematics and allied areas. It is focused on papers dealing with necessary theory and methods in a balanced manner and contributes towards solving problems arising in engineering, control systems, networking system, environment science, health science, physical and biological systems, social issues of current interest, etc.
Computation And Modeling For Fractional Order Systems
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Author : Snehashish Chakraverty
language : en
Publisher: Elsevier
Release Date : 2024-02-20
Computation And Modeling For Fractional Order Systems written by Snehashish Chakraverty and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-20 with Mathematics categories.
Computation and Modeling for Fractional Order Systems provides readers with problem-solving techniques for obtaining exact and/or approximate solutions of governing equations arising in fractional dynamical systems presented using various analytical, semi-analytical, and numerical methods. In this regard, this book brings together contemporary and computationally efficient methods for investigating real-world fractional order systems in one volume. Fractional calculus has gained increasing popularity and relevance over the last few decades, due to its well-established applications in various fields of science and engineering. It deals with the differential and integral operators with non-integral powers. Fractional differential equations are the pillar of various systems occurring in a wide range of science and engineering disciplines, namely physics, chemical engineering, mathematical biology, financial mathematics, structural mechanics, control theory, circuit analysis, and biomechanics, among others. The fractional derivative has also been used in various other physical problems, such as frequency-dependent damping behavior of structures, motion of a plate in a Newtonian fluid, PID controller for the control of dynamical systems, and many others. The mathematical models in electromagnetics, rheology, viscoelasticity, electrochemistry, control theory, Brownian motion, signal and image processing, fluid dynamics, financial mathematics, and material science are well defined by fractional-order differential equations. Generally, these physical models are demonstrated either by ordinary or partial differential equations. However, modeling these problems by fractional differential equations, on the other hand, can make the physics of the systems more feasible and practical in some cases. In order to know the behavior of these systems, we need to study the solutions of the governing fractional models. The exact solution of fractional differential equations may not always be possible using known classical methods. Generally, the physical models occurring in nature comprise complex phenomena, and it is sometimes challenging to obtain the solution (both analytical and numerical) of nonlinear differential equations of fractional order. Various aspects of mathematical modeling that may include deterministic or uncertain (viz. fuzzy or interval or stochastic) scenarios along with fractional order (singular/non-singular kernels) are important to understand the dynamical systems. Computation and Modeling for Fractional Order Systems covers various types of fractional order models in deterministic and non-deterministic scenarios. Various analytical/semi-analytical/numerical methods are applied for solving real-life fractional order problems. The comprehensive descriptions of different recently developed fractional singular, non-singular, fractal-fractional, and discrete fractional operators, along with computationally efficient methods, are included for the reader to understand how these may be applied to real-world systems, and a wide variety of dynamical systems such as deterministic, stochastic, continuous, and discrete are addressed by the authors of the book.
Recent Developments In Theory And Applications Of Fractional Order Systems
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Author : Mehmet Yavuz
language : en
Publisher: Elsevier
Release Date : 2025-09-01
Recent Developments In Theory And Applications Of Fractional Order Systems written by Mehmet Yavuz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-09-01 with Mathematics categories.
Recent Developments in Theory and Applications of Fractional Order Systems presents a rigorous and thorough analysis of various aspects of Fractional Calculus. The book provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines. The authors present each computational modeling concept with a definition, methods, theorems, and observations followed by typical application problems and step-by-step solutions. Each topic is covered in detail, followed typically by several meticulously worked out examples and a problem set containing many additional related problems.In addition, the book discusses recent developments and the latest research on Fractional Calculus and its applications, demonstrating important applications in Engineering, Computer Science, Management, Social Science, and the Humanities. - Provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines - Presents a systematic introduction to most of the important special functions in Fractional Calculus that commonly arise in scientific and engineering practice - Explores many salient computational modeling properties - Analyzes theoretical and practical problems in Fractional Calculus in fields such as Engineering, Computer Science, Management, Social Science, and the Humanities
Viscoelastic Subdiffusive Flows
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Author : Helen Wilson
language : en
Publisher: Springer Nature
Release Date : 2024-12-31
Viscoelastic Subdiffusive Flows written by Helen Wilson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-31 with Technology & Engineering categories.
This book discusses the dynamical and rheological properties of high molecular weight entangled polymer melts, commonly known as viscoelastic subdiffusive fluids. Unlike dilute liquids, these materials exhibit molecular transport within a sublinear regime, meaning the timescale of diffusive transport is sublinear. The text emphasizes the potential of fractional calculus in modeling these fluids and introduces a novel fractional model to investigate regions of spatiotemporal instability in channel flows. At the microscale, the entanglement of polymer chains leads to localized, non-homogeneous regions with increased viscosity, which manifest as spatiotemporal macrostructures at the macroscale. To capture these macrostructures within the flow, direct numerical simulations are employed using a newly developed, physically realizable structure tensor, contributing to a deeper understanding of this complex class of fluids.
Computational Modeling And Sustainable Energy
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Author : Brajesh Kumar Jha
language : en
Publisher: Springer Nature
Release Date : 2025-02-24
Computational Modeling And Sustainable Energy written by Brajesh Kumar Jha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-24 with Computers categories.
This book features best-selected research papers presented at International Conference on Computational Modeling and Sustainable Energy (ICCMSE 2023) held at Pandit Deendayal Energy University, Gandhinagar, Gujarat, India, during December 15–17, 2023. It comprises high-quality research work by academicians and industrial experts in the field of machine learning, mobile computing, natural language processing, fuzzy computing, green computing, human–computer interaction, information retrieval, intelligent control, data mining and knowledge discovery, evolutionary computing, big data, cloud computing, business intelligence, Internet security, pattern recognition, and sustainable energy.
Fractional Integrals And Derivatives Ldquo True Rdquo Versus Ldquo False Rdquo
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Author : Yuri Luchko
language : en
Publisher: MDPI
Release Date : 2021-03-16
Fractional Integrals And Derivatives Ldquo True Rdquo Versus Ldquo False Rdquo written by Yuri Luchko and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-16 with Mathematics categories.
This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.
Applications Of Fractional Calculus To Modeling In Dynamics And Chaos
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Author : J. F. Gómez-Aguilar
language : en
Publisher: CRC Press
Release Date : 2022-09-29
Applications Of Fractional Calculus To Modeling In Dynamics And Chaos written by J. F. Gómez-Aguilar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-29 with Mathematics categories.
Applications of Fractional Calculus to Modeling in Dynamics and Chaos aims to present novel developments, trends, and applications of fractional-order derivatives with power law and Mittag-Leffler kernel in the areas of chemistry, mechanics, chaos, epidemiology, fluid mechanics, modeling, and engineering. Non-singular and non-local fractional-order derivatives have been applied in different chapters to describe complex problems. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate-level students, educators, researchers, and scientists interested in mathematical modeling and its diverse applications. Features Discusses real-world problems, theory, and applications Covers new developments and advances in the various areas of nonlinear dynamics, signal processing, and chaos Suitable to teach master’s and/or PhD-level graduate students, and can be used by researchers, from any field of the social, health, and physical sciences