General Fractional Derivatives with Applications in Viscoelasticity

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

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  • Author : Xiao-Jun Yang
  • Publisher : Academic Press
  • Pages : 454 pages
  • ISBN : 0128172096
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKGeneral Fractional Derivatives with Applications in Viscoelasticity

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
  • Release : 03 April 2020
GET THIS BOOKGeneral Fractional Derivatives with Applications in Viscoelasticity

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

General Fractional Derivatives

General Fractional Derivatives
  • Author : Xiao-Jun Yang
  • Publisher : CRC Press
  • Release : 10 May 2019
GET THIS BOOKGeneral Fractional Derivatives

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

Fractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics
  • Author : Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica
  • Publisher : John Wiley & Sons
  • Release : 19 February 2014
GET THIS BOOKFractional Calculus with Applications in Mechanics

This book contains mathematical preliminaries in which basic definitions of fractional derivatives and spaces are presented. The central part of the book contains various applications in classical mechanics including fields such as: viscoelasticity, heat conduction, wave propagation and variational Hamilton–type principles. Mathematical rigor will be observed in the applications. The authors provide some problems formulated in the classical setting and some in the distributional setting. The solutions to these problems are presented in analytical form and these solutions are

Fractional Calculus and Waves in Linear Viscoelasticity

Fractional Calculus and Waves in Linear Viscoelasticity
  • Author : Francesco Mainardi
  • Publisher : World Scientific
  • Release : 28 February 2021
GET THIS BOOKFractional Calculus and Waves in Linear Viscoelasticity

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

Fractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics
  • Author : Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica
  • Publisher : John Wiley & Sons
  • Release : 17 March 2014
GET THIS BOOKFractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics is the first complete compilation of fractional calculus applications to mechanics. It examines classical mechanics topics, such as viscoelasticity, heat conduction, wave propagation, and variational principles of Hamilton?s type. Author Teodor Atanackovic presents students and researchers in physics, mechanical engineering, and civil engineering with a systematic description of mathematical solutions to mechanical problems.

Advances in Fractional Calculus

Advances in Fractional Calculus
  • Author : J. Sabatier,O. P. Agrawal,J. A. Tenreiro Machado
  • Publisher : Springer Science & Business Media
  • Release : 28 July 2007
GET THIS BOOKAdvances in Fractional Calculus

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the

Fractional Differential Equations

Fractional Differential Equations
  • Author : Igor Podlubny
  • Publisher : Elsevier
  • Release : 27 October 1998
GET THIS BOOKFractional Differential Equations

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

Applications of Fractional Calculus in Physics

Applications of Fractional Calculus in Physics
  • Author : R Hilfer
  • Publisher : World Scientific
  • Release : 02 March 2000
GET THIS BOOKApplications of Fractional Calculus in Physics

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus. This volume provides an introduction to fractional calculus for physicists,

Fractals and Fractional Calculus in Continuum Mechanics

Fractals and Fractional Calculus in Continuum Mechanics
  • Author : Alberto Carpinteri,Francesco Mainardi
  • Publisher : Springer
  • Release : 04 May 2014
GET THIS BOOKFractals and Fractional Calculus in Continuum Mechanics

The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.

Applications in Engineering, Life and Social Sciences

Applications in Engineering, Life and Social Sciences
  • Author : Dumitru Bǎleanu,António Mendes Lopes
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 01 April 2019
GET THIS BOOKApplications in Engineering, Life and Social Sciences

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.

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology
  • Author : Abdon Atangana
  • Publisher : Academic Press
  • Release : 19 September 2017
GET THIS BOOKFractional Operators with Constant and Variable Order with Application to Geo-hydrology

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology provides a physical review of fractional operators, fractional variable order operators, and uncertain derivatives to groundwater flow and environmental remediation. It presents a formal set of mathematical equations for the description of groundwater flow and pollution problems using the concept of non-integer order derivative. Both advantages and disadvantages of models with fractional operators are discussed. Based on the author’s analyses, the book proposes new techniques for groundwater remediation,

Fractional Dynamics

Fractional Dynamics
  • Author : Vasily E. Tarasov
  • Publisher : Springer Science & Business Media
  • Release : 04 January 2011
GET THIS BOOKFractional Dynamics

"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the

Chaos in a Fractional Order Chua System

Chaos in a Fractional Order Chua System
  • Author : Anonim
  • Publisher : Unknown Publisher
  • Release : 28 February 1996
GET THIS BOOKChaos in a Fractional Order Chua System

This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of "order" less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.

Functional Fractional Calculus

Functional Fractional Calculus
  • Author : Shantanu Das
  • Publisher : Springer Science & Business Media
  • Release : 01 June 2011
GET THIS BOOKFunctional Fractional Calculus

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In

Mittag-Leffler Functions, Related Topics and Applications

Mittag-Leffler Functions, Related Topics and Applications
  • Author : Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei V. Rogosin
  • Publisher : Springer
  • Release : 16 October 2014
GET THIS BOOKMittag-Leffler Functions, Related Topics and Applications

As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations