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General Fractional Derivatives with Applications in Viscoelasticity

General Fractional Derivatives with Applications in Viscoelasticity
A Book

by Xiao-Jun Yang,Feng Gao,Yang Ju

  • Publisher : Academic Press
  • Release : 2020-04-03
  • Pages : 454
  • ISBN : 0128172096
  • Language : En, Es, Fr & De
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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

General Fractional Derivatives

General Fractional Derivatives
Theory, Methods and Applications

by Xiao-Jun Yang

  • Publisher : CRC Press
  • Release : 2019-05-10
  • Pages : 364
  • ISBN : 0429811527
  • Language : En, Es, Fr & De
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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.

General Fractional Derivatives

General Fractional Derivatives
Theory, Methods and Applications

by Xiao-Jun Yang

  • Publisher : CRC Press
  • Release : 2019-05-10
  • Pages : 364
  • ISBN : 0429811535
  • Language : En, Es, Fr & De
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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 Calculus and Waves in Linear Viscoelasticity

Fractional Calculus and Waves in Linear Viscoelasticity
An Introduction to Mathematical Models

by Francesco Mainardi

  • Publisher : World Scientific
  • Release : 2010
  • Pages : 368
  • ISBN : 1848163304
  • Language : En, Es, Fr & De
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This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types. It is intended to serve as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature given in the huge general bibliography. This book is likely to be of interest to applied scientists and engineers.

ASME Technical Papers

ASME Technical Papers
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1984
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Modelling of Dynamic Response of Elastomeric Isolation Bearings

Modelling of Dynamic Response of Elastomeric Isolation Bearings
A Book

by Chan Ghee Koh

  • Publisher : Unknown Publisher
  • Release : 1986
  • Pages : 348
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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NASA Conference Publication

NASA Conference Publication
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1991
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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On the Analysis of Structures with Viscoelastic Dampers

On the Analysis of Structures with Viscoelastic Dampers
A Book

by Jose Antonio Inaudi,Alessandra Zambrano,James M. Kelly,University of California, Berkeley. Earthquake Engineering Research Center

  • Publisher : Unknown Publisher
  • Release : 1994
  • Pages : 126
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Archives of Mechanics

Archives of Mechanics
Archiwum Mechaniki Stosowanej

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2008
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Report

Report
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1993
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Distributed-Order Dynamic Systems

Distributed-Order Dynamic Systems
Stability, Simulation, Applications and Perspectives

by Zhuang Jiao,YangQuan Chen,Igor Podlubny

  • Publisher : Springer Science & Business Media
  • Release : 2012-02-24
  • Pages : 90
  • ISBN : 1447128524
  • Language : En, Es, Fr & De
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Distributed-order differential equations, a generalization of fractional calculus, are of increasing importance in many fields of science and engineering from the behaviour of complex dielectric media to the modelling of nonlinear systems. This Brief will broaden the toolbox available to researchers interested in modeling, analysis, control and filtering. It contains contextual material outlining the progression from integer-order, through fractional-order to distributed-order systems. Stability issues are addressed with graphical and numerical results highlighting the fundamental differences between constant-, integer-, and distributed-order treatments. The power of the distributed-order model is demonstrated with work on the stability of noncommensurate-order linear time-invariant systems. Generic applications of the distributed-order operator follow: signal processing and viscoelastic damping of a mass–spring set up. A new general approach to discretization of distributed-order derivatives and integrals is described. The Brief is rounded out with a consideration of likely future research and applications and with a number of MATLAB® codes to reduce repetitive coding tasks and encourage new workers in distributed-order systems.

Science in China

Science in China
Physics, mechanics & astronomy. Series G

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2006-02
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Boundary Element Methods in Applied Mechanics

Boundary Element Methods in Applied Mechanics
Proceedings of the First Joint Japan/US Symposium on Boundary Element Methods, University of Tokyo, Tokyo, Japan, 3-6 October 1988

by Masataka Tanaka,Thomas A. Cruse

  • Publisher : Pergamon
  • Release : 1988
  • Pages : 556
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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This Proceedings features a broad range of computational mechanics papers on both solid and fluid mechanics as well as electromagnetics, acoustics, heat transfer and other interdisciplinary problems. Topics covered include theoretical developments, numerical analysis, intelligent and adaptive solution strategies and practical applications.

A Collection of Technical Papers

A Collection of Technical Papers
AIAA/ASME/ASCE/AHS/ASC 37th Structures, Structural Dynamics and Materials Conference, Salt Lake City, Utah, April 15-17, 1996

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1996
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Fractional and Multivariable Calculus

Fractional and Multivariable Calculus
Model Building and Optimization Problems

by A.M. Mathai,H.J. Haubold

  • Publisher : Springer
  • Release : 2017-07-25
  • Pages : 234
  • ISBN : 3319599933
  • Language : En, Es, Fr & De
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This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable functions). Illustrative examples, input-output process, optimal recovery of functions and approximations are given; each section lists an ample number of exercises to heighten understanding of the material. Chapter three discusses deterministic/mathematical and optimization models evolving from differential equations, difference equations, algebraic models, power function models, input-output models and pathway models. Fractional integral and derivative models are examined. Chapter four covers non-deterministic/stochastic models. The random walk model, branching process model, birth and death process model, time series models, and regression type models are examined. The fifth chapter covers optimal design. General linear models from a statistical point of view are introduced; the Gauss–Markov theorem, quadratic forms, and generalized inverses of matrices are covered. Pathway, symmetric, and asymmetric models are covered in chapter six, the concepts are illustrated with graphs.

Proceedings of IMAC-XIX

Proceedings of IMAC-XIX
A Conference on Structural Dynamics : February 5-8, 2001, Hyatt Orlando, Kissimmee, Florida

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2001
  • Pages : 1773
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Advances in Computational Mechanics

Advances in Computational Mechanics
A Book

by Manolis Papadrakakis,B. H. V. Topping

  • Publisher : Unknown Publisher
  • Release : 1994
  • Pages : 375
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Includes a selection of papers that were presented at the Second International Conference on Computational Structures Technology, held in Athens, Greece, from 30 August - 1 September 1994.

NOISE-CON ... Proceedings

NOISE-CON ... Proceedings
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1991
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Structural Dynamics

Structural Dynamics
Recent Advances : Proceedings of the 5th International Conference

by N. S. Ferguson,Chuh Mei,H. F. Wolfe

  • Publisher : Unknown Publisher
  • Release : 1994
  • Pages : 1108
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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AIAA Journal

AIAA Journal
A Book

by American Institute of Aeronautics and Astronautics

  • Publisher : Unknown Publisher
  • Release : 2003
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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