Handbook Of Fractional Calculus For Engineering And Science

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Handbook of Fractional Calculus for Engineering and Science

Harendra Singh,H. M. Srivastava,Juan J. Nieto
Handbook of Fractional Calculus for Engineering and Science Book PDF

Author : Harendra Singh,H. M. Srivastava,Juan J. Nieto
Publisher : CRC Press
Page : 318 pages
File Size : 44,7 Mb
Release : 2022-02-16
Category : Mathematics
ISBN : 9781000540086

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Handbook of Fractional Calculus for Engineering and Science by Harendra Singh,H. M. Srivastava,Juan J. Nieto Pdf

Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on. This Handbook: Provides reliable methods for solving fractional-order models in science and engineering. Contains efficient numerical methods and algorithms for engineering-related equations. Contains comparison of various methods for accuracy and validity. Demonstrates the applicability of fractional calculus in science and engineering. Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations. Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.

Applications in Engineering, Life and Social Sciences

Dumitru Bǎleanu,António Mendes Lopes
Applications in Engineering Life and Social Sciences Book PDF

Author : Dumitru Bǎleanu,António Mendes Lopes
Publisher : Walter de Gruyter GmbH & Co KG
Page : 256 pages
File Size : 51,8 Mb
Release : 2019-04-01
Category : Mathematics
ISBN : 9783110571905

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Applications in Engineering, Life and Social Sciences by Dumitru Bǎleanu,António Mendes Lopes Pdf

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 seventh volume collects authoritative chapters covering several applications of fractional calculus in in engineering, life, and social sciences, including applications in biology and medicine, mechanics of complex media, economy, and electrical devices.

Applications in Engineering, Life and Social Sciences

Dumitru Baleanu,António Mendes Lopes
Applications in Engineering Life and Social Sciences Book PDF

Author : Dumitru Baleanu,António Mendes Lopes
Publisher : de Gruyter
Page : 0 pages
File Size : 50,9 Mb
Release : 2019
Category : MATHEMATICS
ISBN : 3110570912

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Applications in Engineering, Life and Social Sciences by Dumitru Baleanu,António Mendes Lopes Pdf

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 seventh volume collects authoritative chapters covering several applications of fractional calculus in in engineering, life, and social sciences, including applications in biology and medicine, mechanics of complex media, economy, and electrical devices.

Special Functions in Fractional Calculus and Engineering

Harendra Singh,H M Srivastava,R. K. Pandey
Special Functions in Fractional Calculus and Engineering Book PDF

Author : Harendra Singh,H M Srivastava,R. K. Pandey
Publisher : CRC Press
Page : 315 pages
File Size : 44,9 Mb
Release : 2023-06-29
Category : Technology & Engineering
ISBN : 9781000899757

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Special Functions in Fractional Calculus and Engineering by Harendra Singh,H M Srivastava,R. K. Pandey Pdf

Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations. This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.

Fractional Calculus for Scientists and Engineers

Manuel Duarte Ortigueira
Fractional Calculus for Scientists and Engineers Book PDF

Author : Manuel Duarte Ortigueira
Publisher : Springer
Page : 154 pages
File Size : 54,6 Mb
Release : 2011-06-03
Category : Mathematics
ISBN : 9400707460

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Fractional Calculus for Scientists and Engineers by Manuel Duarte Ortigueira Pdf

This book gives a practical overview of Fractional Calculus as it relates to Signal Processing

Fractional Derivatives with Mittag-Leffler Kernel

José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar
Fractional Derivatives with Mittag Leffler Kernel Book PDF

Author : José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar
Publisher : Springer
Page : 341 pages
File Size : 41,9 Mb
Release : 2019-02-13
Category : Technology & Engineering
ISBN : 9783030116620

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Fractional Derivatives with Mittag-Leffler Kernel by José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar Pdf

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.

Advances in Fractional Calculus

J. Sabatier,O. P. Agrawal,J. A. Tenreiro Machado
Advances in Fractional Calculus Book PDF

Author : J. Sabatier,O. P. Agrawal,J. A. Tenreiro Machado
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 49,8 Mb
Release : 2007-07-28
Category : Technology & Engineering
ISBN : 9781402060427

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Advances in Fractional Calculus by J. Sabatier,O. P. Agrawal,J. A. Tenreiro Machado Pdf

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 book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Fractional Calculus

Dumitru Baleanu,Kai Diethelm,Enrico Scalas,Juan J Trujillo
Fractional Calculus Book PDF

Author : Dumitru Baleanu,Kai Diethelm,Enrico Scalas,Juan J Trujillo
Publisher : World Scientific
Page : 476 pages
File Size : 44,9 Mb
Release : 2016-09-15
Category : Mathematics
ISBN : 9789813140059

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Fractional Calculus by Dumitru Baleanu,Kai Diethelm,Enrico Scalas,Juan J Trujillo Pdf

This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models. All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book will keep in mind the trade-off between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. The second edition of the book has been expanded and now includes a discussion of additional, newly developed numerical methods for fractional calculus and a chapter on the application of fractional calculus for modeling processes in the life sciences.

Mathematical Handbook for Scientists and Engineers

Granino A. Korn,Theresa M. Korn
Mathematical Handbook for Scientists and Engineers Book PDF

Author : Granino A. Korn,Theresa M. Korn
Publisher : Courier Corporation
Page : 1154 pages
File Size : 50,8 Mb
Release : 2013-04-26
Category : Technology & Engineering
ISBN : 9780486320236

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Mathematical Handbook for Scientists and Engineers by Granino A. Korn,Theresa M. Korn Pdf

Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.

Applications in Physics, Part A

Anatoly N. Kochubei,Yurii F. Luchko,Vasily E. Tarasov,Ivo Petráš
Applications in Physics Part A Book PDF

Author : Anatoly N. Kochubei,Yurii F. Luchko,Vasily E. Tarasov,Ivo Petráš
Publisher : de Gruyter
Page : 0 pages
File Size : 41,5 Mb
Release : 2019
Category : Fractional calculus
ISBN : 3110570882

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Applications in Physics, Part A by Anatoly N. Kochubei,Yurii F. Luchko,Vasily E. Tarasov,Ivo Petráš Pdf

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 fourth volume collects authoritative chapters covering several applications of fractional calculus in physics, including classical and continuum mechanics.

Functional Fractional Calculus for System Identification and Controls

Shantanu Das
Functional Fractional Calculus for System Identification and Controls Book PDF

Author : Shantanu Das
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 54,5 Mb
Release : 2007-09-26
Category : Technology & Engineering
ISBN : 9783540727033

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Functional Fractional Calculus for System Identification and Controls by Shantanu Das Pdf

In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.

Fractional Calculus with its Applications in Engineering and Technology

Yi Yang,Haiyan Henry Zhang
Fractional Calculus with its Applications in Engineering and Technology Book PDF

Author : Yi Yang,Haiyan Henry Zhang
Publisher : Morgan & Claypool Publishers
Page : 109 pages
File Size : 52,9 Mb
Release : 2019-03-28
Category : Technology & Engineering
ISBN : 9781681735177

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Fractional Calculus with its Applications in Engineering and Technology by Yi Yang,Haiyan Henry Zhang Pdf

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).

Fractional Calculus: Models And Numerical Methods

Baleanu Dumitru,Diethelm Kai,Scalas Enrico
Fractional Calculus Models And Numerical Methods Book PDF

Author : Baleanu Dumitru,Diethelm Kai,Scalas Enrico
Publisher : World Scientific
Page : 428 pages
File Size : 49,7 Mb
Release : 2012-01-27
Category : Mathematics
ISBN : 9789814458634

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Fractional Calculus: Models And Numerical Methods by Baleanu Dumitru,Diethelm Kai,Scalas Enrico Pdf

The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.

Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering

Praveen Agarwal,Shilpi Jain
Advances in Special Functions of Fractional Calculus Special Functions in Fractional Calculus and Their Applications in Engineering Book PDF

Author : Praveen Agarwal,Shilpi Jain
Publisher : Bentham Science Publishers
Page : 304 pages
File Size : 40,7 Mb
Release : 2023-04-11
Category : Mathematics
ISBN : 9789815079333

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Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering by Praveen Agarwal,Shilpi Jain Pdf

In recent years, special functions have been developed and applied in a variety of fields, such as combinatorics, astronomy, applied mathematics, physics, and engineering due to their remarkable properties. This volume expands our understanding of special functions by highlighting recent trends in numerical analysis. Interesting applications of special functions and partial differential equations are demonstrated by 15 chapters. Many chapters highlight the importance of numerical techniques and the results of complex analysis. Contributions in the book emphasize the mathematical treatment of questions arising in natural sciences and engineering, particularly those that involve novel problems and their solutions. This volume is a timely update for mathematicians and researchers interested in advanced numerical methods and computational techniques used to solve complex problems List of Chapters 1. Modified Adaptive Synchronization and Anti Synchronization method for Fractional order chaotic systems with uncertain parameters 2. Improved generalized differential transform method for a class of linear non homogeneous ordinary fractional differential equation 3. Incomplete K2-Function 4. Some Results On Incomplete Hypergeometric Functions 5. Transcendental Bernstein Series: Interpolation and Approximation 6. Some Sufficient Conditions For Uniform Convexity Of Normalized 1F2 Function 7. From Abel continuity theorem to Paley-Wiener theorem… 8. A New Class of Truncated Exponential-Gould-Hopper basedGenocchi Polynomials 9. Computational preconditioned Gauss-Seidel via half-sweep approximation to Caputo's time fractional differential equations 10. Krasnoselskii-type Theorems for Monotone Operators in Ordered Banach Algebra with Applications in Fractional Differential Equations and Inclusion 11. General fractional order quadratic functional integral equations: Existence, properties of solutions and some of its Applications 12.Nonlinear set-valued delay functional integral equations of Volterra-Stieltjes type: Existence of solutions, continuous dependence and applications 13.Certain Saigo Fractional Derivatives Of Extended Hypergeometric Functions 14. Some Erdelyi-kober Fractional Integrals Of The Extended Hypergeometric Functions 15. On solutions of Kinetic Model by Sumudu transform

Fractional Differential Equations

Anatoly Kochubei,Yuri Luchko
Fractional Differential Equations Book PDF

Author : Anatoly Kochubei,Yuri Luchko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 528 pages
File Size : 41,8 Mb
Release : 2019-02-19
Category : Mathematics
ISBN : 9783110571660

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Fractional Differential Equations by Anatoly Kochubei,Yuri Luchko Pdf

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 second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.