General Fractional Derivatives with Applications in Viscoelasticity
  • Author : Xiao-Jun Yang
  • Release Date : 03 April 2020
  • Publisher : Academic Press
  • Genre : Mathematics
  • Pages : 454
  • ISBN 13 : 9780128172094

Download Or Read General Fractional Derivatives with Applications in Viscoelasticity eBook PDF

Book excerpt: 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 with Applications in Viscoelasticity

General Fractional Derivatives with Applications in Viscoelasticity

Author : Xiao-Jun Yang,Feng Gao,Yang Ju
Publisher : Academic Press
Genre : Mathematics
Get Book

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 ...

General Fractional Derivatives

General Fractional Derivatives

Author : Xiao-Jun Yang
Publisher : CRC Press
Genre : Mathematics
Get Book

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 ...

Applications of Viscoelasticity

Applications of Viscoelasticity

Author : Pouria Hajikarimi,Fereidoon Moghadas Nejad
Publisher : Elsevier
Genre : Technology & Engineering
Get Book

Applications of Viscoelasticity: Bituminous Materials Characterization and Modeling starts with an introduction to the theory of viscoelasticity, emphasizing its importance to various applications in material characterization and modeling. It next looks at constitutive viscoelastic functions, outlines basic equations for different loading conditions, and introduces the Boltzmann superposition principle, relaxation modulus, ...

Methods of Mathematical Modelling and Computation for Complex Systems

Methods of Mathematical Modelling and Computation for Complex Systems

Author : Jagdev Singh,Hemen Dutta,Devendra Kumar,Dumitru Baleanu,Jordan Hristov
Publisher : Springer Nature
Genre : Technology & Engineering
Get Book

This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing ...

Multi Chaos  Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems

Multi Chaos Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems

Author : Yeliz Karaca,Dumitru Baleanu,Yu-Dong Zhang,Osvaldo Gervasi,Majaz Moonis
Publisher : Academic Press
Genre : Science
Get Book

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding ...

Theory and Applications of Special Functions for Scientists and Engineers

Theory and Applications of Special Functions for Scientists and Engineers

Author : Xiao-Jun Yang
Publisher : Springer Nature
Genre : Mathematics
Get Book

This book provides the knowledge of the newly-established supertrigonometric and superhyperbolic functions with the special functions such as Mittag-Leffler, Wiman, Prabhakar, Miller-Ross, Rabotnov, Lorenzo-Hartley, Sonine, Wright and Kohlrausch-Williams-Watts functions, Gauss hypergeometric series and Clausen hypergeometric series. The special functions can be considered to represent a great many of the real-world ...

An Introduction to Hypergeometric  Supertrigonometric  and Superhyperbolic Functions

An Introduction to Hypergeometric Supertrigonometric and Superhyperbolic Functions

Author : Xiao-Jun Yang
Publisher : Academic Press
Genre : Mathematics
Get Book

An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully ...

Fractional Calculus and Waves in Linear Viscoelasticity

Fractional Calculus and Waves in Linear Viscoelasticity

Author : Francesco Mainardi
Publisher : World Scientific
Genre : Science
Get Book

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 ...

Fractional Differential Equations

Fractional Differential Equations

Author : Igor Podlubny
Publisher : Elsevier
Genre : Mathematics
Get Book

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'. ...

Fractional Integrals and Derivatives   ldquo True rdquo  versus  ldquo False rdquo

Fractional Integrals and Derivatives ldquo True rdquo versus ldquo False rdquo

Author : Yuri Luchko
Publisher : MDPI
Genre : Mathematics
Get Book

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?’’, ...

Challenges in Mechanics of Time Dependent Materials  Volume 2

Challenges in Mechanics of Time Dependent Materials Volume 2

Author : H. Jerry Qi,Bonnie Antoun,Richard Hall,Hongbing Lu,Alex Arzoumanidis,Meredith Silberstein,Jevan Furmanski,Alireza Amirkhizi,Joamin Gonzalez-Gutierrez
Publisher : Springer
Genre : Technology & Engineering
Get Book

Challenges in Mechanics of Time-Dependent Materials, Volume 2: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, the second volume of eight from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of ...

Fractional Calculus and Waves in Linear Viscoelasticity

Fractional Calculus and Waves in Linear Viscoelasticity

Author : Francesco Mainardi
Publisher : World Scientific
Genre : Mathematics
Get Book

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 ...

Mittag Leffler Functions  Related Topics and Applications

Mittag Leffler Functions Related Topics and Applications

Author : Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei Rogosin
Publisher : Springer Nature
Genre : Science
Get Book

The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication ...

Theoretical Analyses  Computations  and Experiments of Multiscale Materials

Theoretical Analyses Computations and Experiments of Multiscale Materials

Author : Anonim
Publisher : Springer Nature
Genre : Continuum mechanics
Get Book

This book is devoted to the 60th birthday of the Prof. Francesco dellIsola, who is known for his long-term contribution in the field of multiscale materials. It contains several contributions from researchers in the field, covering theoretical analyses, computational aspects and experiments....

Fractional Derivatives for Physicists and Engineers

Fractional Derivatives for Physicists and Engineers

Author : Vladimir V. Uchaikin
Publisher : Springer Science & Business Media
Genre : Science
Get Book

The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives ...