Intelligent Analysis Fractional Inequalities And Approximations Expanded

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Intelligent Analysis: Fractional Inequalities and Approximations Expanded

Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3030386368
Total Pages : 525 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Intelligent Analysis: Fractional Inequalities and Approximations Expanded by : George A. Anastassiou

Download or read book Intelligent Analysis: Fractional Inequalities and Approximations Expanded written by George A. Anastassiou and published by Springer Nature. This book was released on 2020-01-15 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on computational and fractional analysis, two areas that are very important in their own right, and which are used in a broad variety of real-world applications. We start with the important Iyengar type inequalities and we continue with Choquet integral analytical inequalities, which are involved in major applications in economics. In turn, we address the local fractional derivatives of Riemann–Liouville type and related results including inequalities. We examine the case of low order Riemann–Liouville fractional derivatives and inequalities without initial conditions, together with related approximations. In the next section, we discuss quantitative complex approximation theory by operators and various important complex fractional inequalities. We also cover the conformable fractional approximation of Csiszar’s well-known f-divergence, and present conformable fractional self-adjoint operator inequalities. We continue by investigating new local fractional M-derivatives that share all the basic properties of ordinary derivatives. In closing, we discuss the new complex multivariate Taylor formula with integral remainder. Sharing results that can be applied in various areas of pure and applied mathematics, the book offers a valuable resource for researchers and graduate students, and can be used to support seminars in related fields.

Fractional Inequalities In Banach Algebras

Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3031051483
Total Pages : 312 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Fractional Inequalities In Banach Algebras by : George A. Anastassiou

Download or read book Fractional Inequalities In Banach Algebras written by George A. Anastassiou and published by Springer Nature. This book was released on 2022-05-12 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Fractional Monotone Approximation, Theory and Applications

Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3030959430
Total Pages : 155 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Abstract Fractional Monotone Approximation, Theory and Applications by : George A. Anastassiou

Download or read book Abstract Fractional Monotone Approximation, Theory and Applications written by George A. Anastassiou and published by Springer Nature. This book was released on 2022-03-11 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Banach Space Valued Neural Network

Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3031164008
Total Pages : 429 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Banach Space Valued Neural Network by : George A. Anastassiou

Download or read book Banach Space Valued Neural Network written by George A. Anastassiou and published by Springer Nature. This book was released on 2022-10-01 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Trends in Fractional Differential Equations with Real-World Applications in Physics

Author : Jagdev Singh
Publisher : Frontiers Media SA
ISBN 13 : 2889663043
Total Pages : 172 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis New Trends in Fractional Differential Equations with Real-World Applications in Physics by : Jagdev Singh

Download or read book New Trends in Fractional Differential Equations with Real-World Applications in Physics written by Jagdev Singh and published by Frontiers Media SA. This book was released on 2020-12-30 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.

Parametrized, Deformed and General Neural Networks

Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3031430212
Total Pages : 854 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Parametrized, Deformed and General Neural Networks by : George A. Anastassiou

Download or read book Parametrized, Deformed and General Neural Networks written by George A. Anastassiou and published by Springer Nature. This book was released on 2023-09-29 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Constructive Fractional Analysis with Applications

Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3030714810
Total Pages : 523 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Constructive Fractional Analysis with Applications by : George A. Anastassiou

Download or read book Constructive Fractional Analysis with Applications written by George A. Anastassiou and published by Springer Nature. This book was released on 2021-04-01 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations

Author : George A. Anastassiou
Publisher : Springer
ISBN 13 : 3319669362
Total Pages : 319 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations by : George A. Anastassiou

Download or read book Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations written by George A. Anastassiou and published by Springer. This book was released on 2017-09-02 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book’s results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read independently. This concise book is suitable for use in related graduate classes and many research projects. An extensive list of references is provided for each chapter. The book’s results are relevant for many areas of pure and applied mathematics. As such, it offers a unique resource for researchers, and a valuable addition to all science and engineering libraries.

Intelligent Comparisons: Analytic Inequalities

Author : George A. Anastassiou
Publisher : Springer
ISBN 13 : 3319211218
Total Pages : 662 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Intelligent Comparisons: Analytic Inequalities by : George A. Anastassiou

Download or read book Intelligent Comparisons: Analytic Inequalities written by George A. Anastassiou and published by Springer. This book was released on 2015-07-11 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent and original work of the author on inequalities in real, functional and fractional analysis. The chapters are self-contained and can be read independently, they include an extensive list of references per chapter. The book’s results are expected to find applications in many areas of applied and pure mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, as well as Science and Engineering University libraries.

Intelligent Mathematics: Computational Analysis

Author : George A. Anastassiou
Publisher : Springer Science & Business Media
ISBN 13 : 3642170986
Total Pages : 793 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Intelligent Mathematics: Computational Analysis by : George A. Anastassiou

Download or read book Intelligent Mathematics: Computational Analysis written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2011-03-19 with total page 793 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that Computational Analysis is a very large area with lots of applications. This monograph includes a great variety of topics of Computational Analysis. We present: probabilistic wavelet approximations, constrained abstract approximation theory, shape preserving weighted approximation, non positive approximations to definite integrals, discrete best approximation, approximation theory of general Picard singular operators including global smoothness preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators. We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals. We further deal with semi group operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations. We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities. We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities. We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation \ in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.

Intelligent Comparisons II: Operator Inequalities and Approximations

Author : George A. Anastassiou
Publisher : Springer
ISBN 13 : 331951475X
Total Pages : 224 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Intelligent Comparisons II: Operator Inequalities and Approximations by : George A. Anastassiou

Download or read book Intelligent Comparisons II: Operator Inequalities and Approximations written by George A. Anastassiou and published by Springer. This book was released on 2017-01-13 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.

Intelligent Mathematics II: Applied Mathematics and Approximation Theory

Author : George A. Anastassiou
Publisher : Springer
ISBN 13 : 3319303228
Total Pages : 502 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Intelligent Mathematics II: Applied Mathematics and Approximation Theory by : George A. Anastassiou

Download or read book Intelligent Mathematics II: Applied Mathematics and Approximation Theory written by George A. Anastassiou and published by Springer. This book was released on 2016-03-21 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.

Progress in Approximation Theory and Applicable Complex Analysis

Author : Narendra Kumar Govil
Publisher : Springer
ISBN 13 : 331949242X
Total Pages : 519 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Progress in Approximation Theory and Applicable Complex Analysis by : Narendra Kumar Govil

Download or read book Progress in Approximation Theory and Applicable Complex Analysis written by Narendra Kumar Govil and published by Springer. This book was released on 2017-04-03 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934–2013) of the Université de Montréal. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.

Intelligent Numerical Methods: Applications to Fractional Calculus

Author : George A. Anastassiou
Publisher : Springer
ISBN 13 : 3319267213
Total Pages : 423 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Intelligent Numerical Methods: Applications to Fractional Calculus by : George A. Anastassiou

Download or read book Intelligent Numerical Methods: Applications to Fractional Calculus written by George A. Anastassiou and published by Springer. This book was released on 2015-12-07 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.

Generalized Fractional Calculus

Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3030569624
Total Pages : 501 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Generalized Fractional Calculus by : George A. Anastassiou

Download or read book Generalized Fractional Calculus written by George A. Anastassiou and published by Springer Nature. This book was released on 2020-11-25 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact in numerical analysis, stochastics and fractional differential equations. The book continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities and also includes abstract cases. It presents also multivariate complex Korovkin quantitative approximation theory. It follows M-fractional integral inequalities of Ostrowski and Polya types. The results are weighted so they provide a great variety of cases and applications. The second part of the book deals with the quantitative fractional Korovkin type approximation of stochastic processes and lays there the foundations of stochastic fractional calculus. The book considers both Caputo and Conformable fractional directions and derives regular and trigonometric results. The positive linear operators can be expectation operator commutative or not. This book results are expected to find applications in many areas of pure and applied mathematics and stochastics. As such this monograph is suitable for researchers, graduate students, and seminars of the above disciplines, also to be in all science and engineering libraries.

Intelligent Fractional Order Systems and Control

Author : Indranil Pan
Publisher : Springer
ISBN 13 : 3642315496
Total Pages : 305 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Intelligent Fractional Order Systems and Control by : Indranil Pan

Download or read book Intelligent Fractional Order Systems and Control written by Indranil Pan and published by Springer. This book was released on 2012-08-23 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional order calculus is finding increasing interest in the control system community. Hardware realizations of fractional order controllers have sparked off a renewed zeal into the investigations of control system design in the light of fractional calculus. As such many notions of integer order LTI systems are being modified and extended to incorporate these new concepts. Computational Intelligence (CI) techniques have been applied to engineering problems to find solutions to many hitherto intractable conundrums and is a useful tool for dealing with problems of higher computational complexity. This book borders on the interface between CI techniques and fractional calculus, and looks at ways in which fractional order control systems may be designed or enhanced using CI based paradigms. To the best of the author’s knowledge this is the first book of its kind exclusively dedicated to the application of computational intelligence techniques in fractional order systems and control. The book tries to assimilate various existing concepts in this nascent field of fractional order intelligent control and is aimed at researchers and post graduate students working in this field.

Intelligent Computer Mathematics

Author : Jacques Carette
Publisher : Springer Science & Business Media
ISBN 13 : 3642026141
Total Pages : 510 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Intelligent Computer Mathematics by : Jacques Carette

Download or read book Intelligent Computer Mathematics written by Jacques Carette and published by Springer Science & Business Media. This book was released on 2009-07-06 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: As computers and communications technology advance, greater opportunities arise for intelligent mathematical computation. While computer algebra, au- mated deduction and mathematical publishing each have long and successful histories, we are now seeing increasing opportunities for synergy among them. The Conferences on Intelligent Computer Mathematics (cicm 2009) is a c- lection of co-located meetings, allowing researchers and practitioners active in these related areas to share recent results and identify the next challenges. The speci?c areas of the cicm conferences and workshops are described below, but the unifying theme is the computerized handling of mathematical knowledge. The successful formalization of much of mathematics, as well as a better - derstanding of its internal structure, makes mathematical knowledge in many waysmore tractable than generalknowledge,as traditionally treatedin arti?cial intelligence. Similarly, we can also expect the problem of e?ectively using ma- ematical knowledge in automated ways to be much more tractable. This is the goal of the work in the cicm conferences and workshops. In the long view, so- ing the problems addressed by cicm is an important milestone in formulating the next generation of mathematical software.