General Fractional Derivatives: Theory, Methods and Applications, Xiao-Jun Yang

Автор: Younes Salehi, William E. Schiesser
Название: Numerical Integration of Space Fractional Partial Differential Equations, Volume 2: Applications from Classical Integer PDEs
ISBN: 1681732092 ISBN-13(EAN): 9781681732091
Издательство: Mare Nostrum (Eurospan)
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Цена: 82230.00 T
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Описание: Partial differential equations are one of the most used widely forms of mathematics in science and engineering. Two fractional PDEs can be considered, fractional in time, and fractional in space. This volume is directed to the development and use of SFPDEs, providing a discussion of applications from classical integer PDEs.

Автор: Younes Salehi, William E. Schiesser
Название: Numerical Integration of Space Fractional Partial Differential Equations, Volume 2: Applications from Classical Integer PDEs
ISBN: 1681732718 ISBN-13(EAN): 9781681732718
Издательство: Mare Nostrum (Eurospan)
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Цена: 108110.00 T
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Описание: Partial differential equations are one of the most used widely forms of mathematics in science and engineering. Two fractional PDEs can be considered, fractional in time, and fractional in space. This volume is directed to the development and use of SFPDEs, providing an introduction to Algorithms and Computer Coding in R.

Автор: Yi Yang, Haiyan Henry Zhang
Название: Fractional Calculus with its Applications in Engineering and Technology
ISBN: 1681735180 ISBN-13(EAN): 9781681735184
Издательство: Mare Nostrum (Eurospan)
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Цена: 61910.00 T
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Описание: 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).

Автор: Yi Yang, Haiyan Henry Zhang
Название: Fractional Calculus with its Applications in Engineering and Technology
ISBN: 1681735164 ISBN-13(EAN): 9781681735160
Издательство: Mare Nostrum (Eurospan)
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Цена: 41580.00 T
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Описание: 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).

Автор: Yang, Xiao-Jun
Название: General Fractional Derivatives With Applications In Viscoelasticity
ISBN: 0128172088 ISBN-13(EAN): 9780128172087
Издательство: Elsevier Science
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Цена: 132500.00 T
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General Fractional Derivatives with Applications in Viscoelasticity introduces the newly established fractional-order calculus operators involving singular and non-singular kernels with applications to fractional-order viscoelastic models from the calculus operator viewpoint. Fractional calculus and its applications have gained considerable popularity and importance because of their applicability to many seemingly diverse and widespread fields in science and engineering. Many operations in physics and engineering can be defined accurately by using fractional derivatives to model complex phenomena. Viscoelasticity is chief among them, as the general fractional calculus approach to viscoelasticity has evolved as an empirical method of describing the properties of viscoelastic materials. General Fractional Derivatives with Applications in Viscoelasticity makes a concise presentation of general fractional calculus.

• Presents a comprehensive overview of the fractional derivatives and their applications in viscoelasticity
• Provides help in handling the power-law functions
• Introduces and explores the questions about general fractional derivatives and its applications

Автор: Fallahgoul, Hassan
Название: Fractional Calculus and Fractional Processes with Applications to
ISBN: 0128042486 ISBN-13(EAN): 9780128042489
Издательство: Elsevier Science
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Цена: 61760.00 T
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Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization.

Автор: Xiao Jun Yang
Название: Local Fractional Integral Transforms and Their Applications
ISBN: 0128040025 ISBN-13(EAN): 9780128040027
Издательство: Elsevier Science
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Цена: 77470.00 T
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Описание: Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms.

• Provides applications of local fractional Fourier Series
• Discusses definitions for local fractional Laplace transforms
• Explains local fractional Laplace transforms coupled with analytical methods

Автор: Lorenzo
Название: The Fractional Trigonometry - With Applications to Fractional Differential Equations and Science
ISBN: 1119139406 ISBN-13(EAN): 9781119139409
Издательство: Wiley
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Цена: 124550.00 T
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Описание: Classical trigonometry plays a very important role relative to integer order calculus, and together with the common exponential function, provides solutions for linear differential equations.

Автор: Changpin Li, Min Cai
Название: Theory and Numerical Approximations of Fractional Integrals and Derivatives
ISBN: 1611975875 ISBN-13(EAN): 9781611975871
Издательство: Mare Nostrum (Eurospan)
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Цена: 76910.00 T
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Описание: Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus and provides a detailed treatment of existing numerical approximations.Theory and Numerical Approximations of Fractional Integrals and Derivatives presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results.The book’s core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.

Автор: George A. Anastassiou; Ioannis K. Argyros
Название: Functional Numerical Methods: Applications to Abstract Fractional Calculus
ISBN: 3319695258 ISBN-13(EAN): 9783319695259
Издательство: Springer
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Цена: 111790.00 T
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Описание: Explicit-Implicit methods with applications to Banach space valued functions in abstract fractional calculus.- Convergence of Iterative methods in abstract fractional calculus.- Equations for Banach space valued functions in fractional vector calculi.- Iterative methods in abstract fractional calculus.- Semi-local convergence in right abstract fractional calculus.- Algorithmic convergence in abstract g-fractional calculus.- Iterative procedures for solving equations in abstract fractional calculus.- Approximate solutions of equations in abstract g-fractional calculus.- Generating sequences for solving in abstract g-fractional calculus.- Numerical Optimization and fractional invexity.

Автор: Dumitru Baleanu and Antonio Mendes Lopes
Название: Handbook of Fractional Calculus with Applications
ISBN: 3110570920 ISBN-13(EAN): 9783110570922
Издательство: Walter de Gruyter
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Цена: 149590.00 T
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Описание: 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 eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.

Автор: Jos? Francisco G?mez; Lizeth Torres; Ricardo Fabri
Название: Fractional Derivatives with Mittag-Leffler Kernel
ISBN: 3030116611 ISBN-13(EAN): 9783030116613
Издательство: Springer
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Цена: 93160.00 T
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Описание: 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.