Constructive Fractional Analysis With Applications

Author : George A. Anastassiou
Publisher : Springer Nature
Page : 523 pages
File Size : 53,5 Mb
Release : 2021-04-01
Category : Technology & Engineering
ISBN : 9783030714819

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Constructive Fractional Analysis with Applications by George A. Anastassiou Pdf

This book includes constructive approximation theory; it presents ordinary and fractional approximations by positive sublinear operators, and high order approximation by multivariate generalized Picard, Gauss–Weierstrass, Poisson–Cauchy and trigonometric singular integrals. Constructive and Computational Fractional Analysis recently is more and more in the center of mathematics because of their great applications in the real world. In this book, all presented is original work by the author given at a very general level to cover a maximum number of cases in various applications. The author applies generalized fractional differentiation techniques of Riemann–Liouville, Caputo and Canavati types and of fractional variable order to various kinds of inequalities such as of Opial, Hardy, Hilbert–Pachpatte and on the spherical shell. He continues with E. R. Love left- and right-side fractional integral inequalities. They follow fractional Landau inequalities, of left and right sides, univariate and multivariate, including ones for Semigroups. These are developed to all possible directions, and right-side multivariate fractional Taylor formulae are proven for the purpose. It continues with several Gronwall fractional inequalities of variable order. This book results are expected to find applications in many areas of pure and applied mathematics. As such this book is suitable for researchers, graduate students and seminars of the above disciplines, also to be in all science and engineering libraries.

Author : George A. Anastassiou
Publisher : Springer Nature
Page : 155 pages
File Size : 41,8 Mb
Release : 2022-03-11
Category : Technology & Engineering
ISBN : 9783030959432

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Abstract Fractional Monotone Approximation, Theory and Applications by George A. Anastassiou Pdf

This book employs an abstract kernel fractional calculus with applications to Prabhakar and non-singular kernel fractional calculi. The results are univariate and bivariate. In the univariate case, abstract fractional monotone approximation by polynomials and splines is presented. In the bivariate case, the abstract fractional monotone constrained approximation by bivariate pseudo-polynomials and polynomials is given. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional approximation and fractional differential equations. Other interesting applications are applied in sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines.

Author : George A. Anastassiou
Publisher : Springer Nature
Page : 312 pages
File Size : 53,8 Mb
Release : 2022-05-12
Category : Technology & Engineering
ISBN : 9783031051487

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Fractional Inequalities In Banach Algebras by George A. Anastassiou Pdf

This book presents generalized Caputo fractional Ostrowski and Grüss-type inequalities involving several Banach algebra valued functions. Furthermore, the author gives generalized Canavati fractional Ostrowski, Opial, Grüss, and Hilbert-Pachpatte-type inequalities for multiple Banach algebra valued functions. By applying the p-Schatten norms over the von Neumann–Schatten classes, the author produces the analogous refined and interesting inequalities. The author provides many applications. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications are in applied sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.

Author : Ivanka Stamova,Gani Stamov
Publisher : CRC Press
Page : 134 pages
File Size : 45,5 Mb
Release : 2017-03-03
Category : Mathematics
ISBN : 9781315350448

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Functional and Impulsive Differential Equations of Fractional Order by Ivanka Stamova,Gani Stamov Pdf

The book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by demonstrating how these techniques can be applied to investigate qualitative properties of the solutions of fractional systems. Since many applications have been included, the demonstrated techniques and models can be used in training students in mathematical modeling and in the study and development of fractional-order models.

Author : George A. Anastassiou
Publisher : Springer Nature
Page : 854 pages
File Size : 55,6 Mb
Release : 2023-09-29
Category : Technology & Engineering
ISBN : 9783031430213

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Parametrized, Deformed and General Neural Networks by George A. Anastassiou Pdf

In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.

Author : George A. Anastassiou
Publisher : Springer Nature
Page : 429 pages
File Size : 55,8 Mb
Release : 2022-10-01
Category : Technology & Engineering
ISBN : 9783031164002

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Banach Space Valued Neural Network by George A. Anastassiou Pdf

This book is about the generalization and modernization of approximation by neural network operators. Functions under approximation and the neural networks are Banach space valued. These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. Ordinary, fractional, fuzzy, and stochastic approximations are exhibited at the univariate, fractional, and multivariate levels. Iterated-sequential approximations are also covered. The book’s results are expected to find applications in the many areas of applied mathematics, computer science and engineering, especially in artificial intelligence and machine learning. Other possible applications can be in applied sciences like statistics, economics, etc. Therefore, this book is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.

Author : Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 41,9 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9781119654162

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Fractional Order Analysis by Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana Pdf

A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.

Author : Michel A. Théra
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 55,8 Mb
Release : 2000
Category : Mathematics
ISBN : 0821821679

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Constructive, Experimental, and Nonlinear Analysis by Michel A. Théra Pdf

"This volume presents twenty original refereed papers on different aspects of modern analysis, including analytic and computational number theory, symbolic and numerical computation, theoretical and computational optimization, and recent development in nonsmooth and functional analysis with applications to control theory. These papers originated largely from a conference held in conjunction with a 1999 Doctorate Honoris Causa awarded to Jonathan Borwein at Limoges. As such they reflect the areas in which Dr. Borwein has worked. In addition to providing a snapshot of research in the field of modern analysis, the papers suggest some of the directions this research is following at the beginning of the millennium."--BOOK JACKET.

Author : J. F. Gómez-Aguilar,Abdon Atangana
Publisher : CRC Press
Page : 511 pages
File Size : 43,9 Mb
Release : 2022-09-29
Category : Mathematics
ISBN : 9781000597615

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Applications of Fractional Calculus to Modeling in Dynamics and Chaos by J. F. Gómez-Aguilar,Abdon Atangana Pdf

Applications of Fractional Calculus to Modeling in Dynamics and Chaos aims to present novel developments, trends, and applications of fractional-order derivatives with power law and Mittag-Leffler kernel in the areas of chemistry, mechanics, chaos, epidemiology, fluid mechanics, modeling, and engineering. Non-singular and non-local fractional-order derivatives have been applied in different chapters to describe complex problems. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate-level students, educators, researchers, and scientists interested in mathematical modeling and its diverse applications. Features Discusses real-world problems, theory, and applications Covers new developments and advances in the various areas of nonlinear dynamics, signal processing, and chaos Suitable to teach master’s and/or PhD-level graduate students, and can be used by researchers, from any field of the social, health, and physical sciences

Author : Francesco Mainardi
Publisher : MDPI
Page : 209 pages
File Size : 40,5 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 : Kai Diethelm
Publisher : Springer
Page : 247 pages
File Size : 43,5 Mb
Release : 2010-08-18
Category : Mathematics
ISBN : 9783642145742

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The Analysis of Fractional Differential Equations by Kai Diethelm Pdf

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Author : Hasan Fallahgoul,Sergio Focardi,Frank Fabozzi
Publisher : Academic Press
Page : 118 pages
File Size : 43,6 Mb
Release : 2016-10-06
Category : Mathematics
ISBN : 9780128042847

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Fractional Calculus and Fractional Processes with Applications to Financial Economics by Hasan Fallahgoul,Sergio Focardi,Frank Fabozzi Pdf

Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization. Provides the necessary background for the book's content as applied to financial economics Analyzes the application of fractional calculus and fractional processes from deterministic and stochastic perspectives

Author : Rudolf Hilfer
Publisher : World Scientific
Page : 473 pages
File Size : 49,7 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 : 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 : B. Ross
Publisher : Springer
Page : 391 pages
File Size : 52,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540699750

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Fractional Calculus and Its Applications by B. Ross Pdf