Ordinary And Fractional Approximation By Non Additive Integrals Choquet Shilkret And Sugeno Integral Approximators
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Ordinary And Fractional Approximation By Non Additive Integrals Choquet Shilkret And Sugeno Integral Approximators
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Author : George A. Anastassiou
language : en
Publisher: Springer
Release Date : 2018-12-07
Ordinary And Fractional Approximation By Non Additive Integrals Choquet Shilkret And Sugeno Integral Approximators written by George A. Anastassiou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Technology & Engineering categories.
Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences. The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book’s findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.
Ordinary And Fractional Approximation By Non Additive Integrals
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Author : George A. Anastassiou
language : en
Publisher:
Release Date : 2019
Ordinary And Fractional Approximation By Non Additive Integrals written by George A. Anastassiou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Approximation theory categories.
Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences.
Banach Space Valued Neural Network
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2022-10-01
Banach Space Valued Neural Network written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-01 with Technology & Engineering categories.
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.
Abstract Fractional Monotone Approximation Theory And Applications
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2022-03-11
Abstract Fractional Monotone Approximation Theory And Applications written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-11 with Technology & Engineering categories.
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.
Fractional Inequalities In Banach Algebras
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2022-05-12
Fractional Inequalities In Banach Algebras written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-12 with Technology & Engineering categories.
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.
Parametrized Deformed And General Neural Networks
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2023-09-29
Parametrized Deformed And General Neural Networks written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-29 with Technology & Engineering categories.
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.
Fractional Order Analysis
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Author : Hemen Dutta
language : en
Publisher: John Wiley & Sons
Release Date : 2020-08-06
Fractional Order Analysis written by Hemen Dutta and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-06 with Mathematics categories.
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.
Nature S Patterns And The Fractional Calculus
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Author : Bruce J. West
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-09-11
Nature S Patterns And The Fractional Calculus written by Bruce J. West and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.
Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus
New Numerical Scheme With Newton Polynomial
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Author : Abdon Atangana
language : en
Publisher: Academic Press
Release Date : 2021-06-10
New Numerical Scheme With Newton Polynomial written by Abdon Atangana and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-10 with Mathematics categories.
New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications provides a detailed discussion on the underpinnings of the theory, methods and real-world applications of this numerical scheme. The book's authors explore how this efficient and accurate numerical scheme is useful for solving partial and ordinary differential equations, as well as systems of ordinary and partial differential equations with different types of integral operators. Content coverage includes the foundational layers of polynomial interpretation, Lagrange interpolation, and Newton interpolation, followed by new schemes for fractional calculus. Final sections include six chapters on the application of numerical scheme to a range of real-world applications. Over the last several decades, many techniques have been suggested to model real-world problems across science, technology and engineering. New analytical methods have been suggested in order to provide exact solutions to real-world problems. Many real-world problems, however, cannot be solved using analytical methods. To handle these problems, researchers need to rely on numerical methods, hence the release of this important resource on the topic at hand. - Offers an overview of the field of numerical analysis and modeling real-world problems - Provides a deeper understanding and comparison of Adams-Bashforth and Newton polynomial numerical methods - Presents applications of local fractional calculus to a range of real-world problems - Explores new scheme for fractal functions and investigates numerical scheme for partial differential equations with integer and non-integer order - Includes codes and examples in MATLAB in all relevant chapters
Distributions In The Physical And Engineering Sciences Volume 3
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Author : Alexander I. Saichev
language : en
Publisher: Birkhäuser
Release Date : 2018-08-03
Distributions In The Physical And Engineering Sciences Volume 3 written by Alexander I. Saichev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-03 with Mathematics categories.
Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.