Fractional And Multivariable Calculus

Author : A.M. Mathai,H.J. Haubold
Publisher : Springer
Page : 234 pages
File Size : 55,8 Mb
Release : 2017-07-25
Category : Mathematics
ISBN : 9783319599939

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Fractional and Multivariable Calculus by A.M. Mathai,H.J. Haubold Pdf

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.

Author : Virginia S Kiryakova
Publisher : CRC Press
Page : 412 pages
File Size : 43,8 Mb
Release : 1993-12-27
Category : Mathematics
ISBN : 0582219779

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Generalized Fractional Calculus and Applications by Virginia S Kiryakova Pdf

In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.

Author : Mathai Arak M,Haubold Hans J
Publisher : World Scientific
Page : 292 pages
File Size : 40,8 Mb
Release : 2017-11-10
Category : Mathematics
ISBN : 9789813227545

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Matrix Methods And Fractional Calculus by Mathai Arak M,Haubold Hans J Pdf

Fractional calculus in terms of mathematics and statistics and its applications to problems in natural sciences is NOT yet part of university teaching curricula. This book is one attempt to provide an approach to include topics of fractional calculus into university curricula. Additionally the material is useful for people who do research work in the areas of special functions, fractional calculus, applications of fractional calculus, and mathematical statistics. Contents: PrefaceList of SymbolsVector/Matrix Derivatives and OptimizationJacobians of Matrix Transformations and Functions of Matrix ArgumentFractional Calculus and Special FunctionsFractional Calculus and Fractional Differential EquationsKober Fractional Calculus and Matrix-Variate FunctionsLie Theory and Special FunctionsSelected Topics in Multivariate Analysis Readership: Graduate students and researchers in all aspects of fractional calculus and its applications. Keywords: Vector/Matrix Derivatives;Optimization;Jacobians of Matrix Transformations;Multivariate Analysis;Functions of Matrix Argument;Fractional Calculus;Special Functions;Lie Theory;Fractional Differential Equations;Kober Fractional Calculus;Matrix-Variate FunctionsReview:0

Author : Dumitru Baleanu,Kai Diethelm,Enrico Scalas,Juan J Trujillo
Publisher : World Scientific
Page : 476 pages
File Size : 42,8 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.

Author : Baleanu Dumitru,Diethelm Kai,Scalas Enrico
Publisher : World Scientific
Page : 428 pages
File Size : 50,9 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.

Author : Francesco Mainardi
Publisher : MDPI
Page : 209 pages
File Size : 44,7 Mb
Release : 2018-09-20
Category : Electronic books
ISBN : 9783038972068

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Fractional Calculus: Theory and Applications by Francesco Mainardi Pdf

This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics

Author : George A. Anastassiou
Publisher : Springer Science & Business Media
Page : 123 pages
File Size : 48,7 Mb
Release : 2011-07-25
Category : Mathematics
ISBN : 9781461407034

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Advances on Fractional Inequalities by George A. Anastassiou Pdf

Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given. Fractional differentiation inequalities are by themselves an important and great mathematical topic for research. Furthermore they have many applications, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations. Also they provide upper bounds to the solutions of the above equations. Fractional Calculus has emerged as very useful over the last forty years due to its many applications in almost all applied sciences. This is currently seen in applications in acoustic wave propagation in inhomogeneous porous material, diffusive transport, fluid flow, dynamical processes in self-similar structures, dynamics of earthquakes, optics, geology, viscoelastic materials, bio-sciences, bioengineering, medicine, economics, probability and statistics, astrophysics, chemical engineering, physics, splines, tomography, fluid mechanics, electromagnetic waves, nonlinear control, signal processing, control of power electronic, converters, chaotic dynamics, polymer science, proteins, polymer physics, electrochemistry, statistical physics, rheology, thermodynamics, neural networks, etc. Almost all fields of research in science and engineering use fractional calculus in order to describe results. This book is a part of Fractional Calculus, therefore it is useful for researchers and graduate students for research, seminars and advanced graduate courses, in pure and applied mathematics, engineering and all other applied sciences.

Author : B. Ross
Publisher : Unknown
Page : 396 pages
File Size : 54,7 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662176998

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Fractional Calculus and Its Applications by B. Ross Pdf

Author : Michal Fečkan,JinRong Wang,Michal Pospíšil
Publisher : Walter de Gruyter GmbH & Co KG
Page : 383 pages
File Size : 45,8 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783110521559

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Fractional-Order Equations and Inclusions by Michal Fečkan,JinRong Wang,Michal Pospíšil Pdf

This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions

Author : A. M. Mathai,H. J. Haubold
Publisher : Springer
Page : 122 pages
File Size : 46,8 Mb
Release : 2018-09-06
Category : Science
ISBN : 9789811311598

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Erdélyi–Kober Fractional Calculus by A. M. Mathai,H. J. Haubold Pdf

This book focuses on Erdélyi–Kober fractional calculus from a statistical perspective inspired by solar neutrino physics. Results of diffusion entropy analysis and standard deviation analysis of data from the Super-Kamiokande solar neutrino experiment lead to the development of anomalous diffusion and reaction in terms of fractional calculus. The new statistical perspective of Erdélyi–Kober fractional operators outlined in this book will have fundamental applications in the theory of anomalous reaction and diffusion processes dealt with in physics. A major mathematical objective of this book is specifically to examine a new definition for fractional integrals in terms of the distributions of products and ratios of statistically independently distributed positive scalar random variables or in terms of Mellin convolutions of products and ratios in the case of real scalar variables. The idea will be generalized to cover multivariable cases as well as matrix variable cases. In the matrix variable case, M-convolutions of products and ratios will be used to extend the ideas. We then give a definition for the case of real-valued scalar functions of several matrices.

Author : Rudolf Hilfer
Publisher : World Scientific
Page : 473 pages
File Size : 54,8 Mb
Release : 2000-03-02
Category : Science
ISBN : 9789814496209

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Applications Of Fractional Calculus In Physics by Rudolf Hilfer Pdf

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, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.

Author : Gary Francis Roach
Publisher : Pitman Advanced Publishing Program
Page : 228 pages
File Size : 52,9 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39076000556477

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Fractional Calculus by Gary Francis Roach Pdf

Author : H. M. Srivastava,Shigeyoshi Owa
Publisher : Chichester : Ellis Horwood ; New York ; Toronto : Halsted Press
Page : 416 pages
File Size : 48,6 Mb
Release : 1989
Category : Calculus
ISBN : UCAL:B4406327

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Univalent Functions, Fractional Calculus, and Their Applications by H. M. Srivastava,Shigeyoshi Owa Pdf

Author : Keith B. Oldham,Jerome Spanier
Publisher : Unknown
Page : 234 pages
File Size : 50,5 Mb
Release : 1974
Category : Calculus
ISBN : 0125355505

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The Fractional Calculus by Keith B. Oldham,Jerome Spanier Pdf

Author : Changpin Li,Fanhai Zeng
Publisher : CRC Press
Page : 300 pages
File Size : 45,8 Mb
Release : 2015-05-19
Category : Mathematics
ISBN : 9781482253818

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Numerical Methods for Fractional Calculus by Changpin Li,Fanhai Zeng Pdf

Numerical Methods for Fractional Calculus presents numerical methods for fractional integrals and fractional derivatives, finite difference methods for fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs), and finite element methods for FPDEs.The book introduces the basic definitions and propertie