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Advanced Applications of Fractional Differential Operators to Science and Technology

Advanced Applications of Fractional Differential Operators to Science and Technology
Author: Matouk, Ahmed Ezzat
Publisher: IGI Global
Total Pages: 401
Release: 2020-04-24
Genre: Mathematics
ISBN: 1799831248
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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.

Theory and Applications of Fractional Differential Equations

Theory and Applications of Fractional Differential Equations
Author: A.A. Kilbas
Publisher: Elsevier
Total Pages: 550
Release: 2006-02-16
Genre: Mathematics
ISBN: 9780444518323
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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.

Advances on Fractional Inequalities

Advances on Fractional Inequalities
Author: George A. Anastassiou
Publisher: Springer Science & Business Media
Total Pages: 123
Release: 2011-07-25
Genre: Mathematics
ISBN: 1461407036
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Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given. Fractional differentiation inequalities are by themselves an important and great mathematical topic for research. Furthermore they have many applications, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations. Also they provide upper bounds to the solutions of the above equations. Fractional Calculus has emerged as very useful over the last forty years due to its many applications in almost all applied sciences. This is currently seen in applications in acoustic wave propagation in inhomogeneous porous material, diffusive transport, fluid flow, dynamical processes in self-similar structures, dynamics of earthquakes, optics, geology, viscoelastic materials, bio-sciences, bioengineering, medicine, economics, probability and statistics, astrophysics, chemical engineering, physics, splines, tomography, fluid mechanics, electromagnetic waves, nonlinear control, signal processing, control of power electronic, converters, chaotic dynamics, polymer science, proteins, polymer physics, electrochemistry, statistical physics, rheology, thermodynamics, neural networks, etc. Almost all fields of research in science and engineering use fractional calculus in order to describe results. This book is a part of Fractional Calculus, therefore it is useful for researchers and graduate students for research, seminars and advanced graduate courses, in pure and applied mathematics, engineering and all other applied sciences.

General Fractional Derivatives

General Fractional Derivatives
Author: Xiao-Jun Yang
Publisher: CRC Press
Total Pages: 306
Release: 2019-05-10
Genre: Mathematics
ISBN: 0429811527
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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.

Fractional Derivatives with Mittag-Leffler Kernel

Fractional Derivatives with Mittag-Leffler Kernel
Author: José Francisco Gómez
Publisher: Springer
Total Pages: 341
Release: 2019-02-13
Genre: Technology & Engineering
ISBN: 303011662X
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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.

Fractional Calculus

Fractional Calculus
Author: Roy Abi Zeid Daou
Publisher: Nova Science Publishers
Total Pages: 0
Release: 2014-01-11
Genre: Fractional calculus
ISBN: 9781634630023
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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.

Fractional Differential Equations

Fractional Differential Equations
Author: Igor Podlubny
Publisher: Elsevier
Total Pages: 366
Release: 1998-10-27
Genre: Mathematics
ISBN: 0080531989
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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

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics
Author: Elina Shishkina
Publisher: Academic Press
Total Pages: 594
Release: 2020-07-24
Genre: Mathematics
ISBN: 0128204079
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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. Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details Enables researchers, lecturers and students to find material under the single "roof"

Research Advancements in Smart Technology, Optimization, and Renewable Energy

Research Advancements in Smart Technology, Optimization, and Renewable Energy
Author: Vasant, Pandian
Publisher: IGI Global
Total Pages: 407
Release: 2020-08-07
Genre: Technology & Engineering
ISBN: 1799839710
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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.

Handbook of Research on Engineering Innovations and Technology Management in Organizations

Handbook of Research on Engineering Innovations and Technology Management in Organizations
Author: Gaur, Loveleen
Publisher: IGI Global
Total Pages: 459
Release: 2020-04-17
Genre: Technology & Engineering
ISBN: 1799827739
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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.