Nonlocal Nonlinear Fractional Order Boundary Value Problems

Author : Bashir Ahmad,Sotiris K Ntouyas
Publisher : World Scientific
Page : 597 pages
File Size : 42,7 Mb
Release : 2021-04-06
Category : Mathematics
ISBN : 9789811230424

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Nonlocal Nonlinear Fractional-order Boundary Value Problems by Bashir Ahmad,Sotiris K Ntouyas Pdf

There has been a great advancement in the study of fractional-order nonlocal nonlinear boundary value problems during the last few decades. The interest in the subject of fractional-order boundary value problems owes to the extensive application of fractional differential equations in many engineering and scientific disciplines. Fractional-order differential and integral operators provide an excellent instrument for the description of memory and hereditary properties of various materials and processes, which contributed significantly to the popularity of the subject and motivated many researchers and modelers to shift their focus from classical models to fractional order models. Some peculiarities of physical, chemical or other processes happening inside the domain cannot be formulated with the aid of classical boundary conditions. This limitation led to the consideration of nonlocal and integral conditions which relate the boundary values of the unknown function to its values at some interior positions of the domain.The main objective for writing this book is to present some recent results on single-valued and multi-valued boundary value problems, involving different kinds of fractional differential and integral operators, and several kinds of nonlocal multi-point, integral, integro-differential boundary conditions. Much of the content of this book contains the recent research published by the authors on the topic.

Author : Bashir Ahmad (Mathematics professor),Sotiris K. Ntouyas
Publisher : Unknown
Page : 0 pages
File Size : 48,6 Mb
Release : 2021
Category : Electronic books
ISBN : 9811230412

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Nonlocal Nonlinear Fractional-order Boundary Value Problems by Bashir Ahmad (Mathematics professor),Sotiris K. Ntouyas Pdf

"There has been a great advancement in the study of fractional-order nonlocal nonlinear boundary value problems during the last few decades. The interest in the subject of fractional-order boundary value problems owes to the extensive application of fractional differential equations in many engineering and scientific disciplines. Fractional-order differential and integral operators provide an excellent instrument for the description of memory and hereditary properties of various materials and processes, which contributed significantly to the popularity of the subject and motivated many researchers and modelers to shift their focus from classical models to fractional order models. Some peculiarities of physical, chemical or other processes happening inside the domain cannot be formulated with the aid of classical boundary conditions. This limitation led to the consideration of nonlocal and integral conditions which relate the boundary values of the unknown function to its values at some interior positions of the domain. The main objective for writing this book is to present some recent results on single-valued and multi-valued boundary value problems, involving different kinds of fractional differential and integral operators, and several kinds of nonlocal multi-point, integral, integro-differential boundary conditions. Much of the content of this book contains the recent research published by the authors on the topic"--

Author : Alain Berlinet,Christine Thomas-Agnan
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 53,8 Mb
Release : 2011-06-28
Category : Business & Economics
ISBN : 9781441990969

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Reproducing Kernel Hilbert Spaces in Probability and Statistics by Alain Berlinet,Christine Thomas-Agnan Pdf

The book covers theoretical questions including the latest extension of the formalism, and computational issues and focuses on some of the more fruitful and promising applications, including statistical signal processing, nonparametric curve estimation, random measures, limit theorems, learning theory and some applications at the fringe between Statistics and Approximation Theory. It is geared to graduate students in Statistics, Mathematics or Engineering, or to scientists with an equivalent level.

Author : Paul W. Eloe,Johnny Henderson
Publisher : World Scientific
Page : 249 pages
File Size : 42,8 Mb
Release : 2016
Category : Mathematics
ISBN : 9789814733489

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Nonlinear Interpolation and Boundary Value Problems by Paul W. Eloe,Johnny Henderson Pdf

"This book is devoted to the study of solutions of nonlinear ODE boundary value problems as nonlinear interpolation problems. In 1967, Lasota and Opial showed that, under suitable hypotheses, if solutions of a second-order nonlinear differential equation passing through two distinct points are unique, when they exist, then, in fact, a solution passing through two distinct points does exist. That result, coupled with the pioneering work of Philip Hartman on what was then called unrestricted n-parameter families has stimulated 50 years of rapid development in the study of solutions of boundary value problems as nonlinear interpolation problems. The purpose of this book is two-fold. First, the results that have been generated in the past 50 years are collected for the first time to produce a comprehensive and coherent treatment of what is now a well-defined area of study in the qualitative theory of ordinary differential equations. Second, methods and technical tools are sufficiently exposed so that the interested reader can contribute to the study of nonlinear interpolation"--

Author : V. P. Mikhailov
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 51,6 Mb
Release : 1975
Category : Mathematics
ISBN : 0821830260

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Boundary Value Problems for Differential Equations by V. P. Mikhailov Pdf

Author : Sotiris K. Ntouyas
Publisher : MDPI
Page : 518 pages
File Size : 54,6 Mb
Release : 2020-11-09
Category : Mathematics
ISBN : 9783039432189

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Fractional Differential Equations, Inclusions and Inequalities with Applications by Sotiris K. Ntouyas Pdf

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.

Author : H. M. Srivastava
Publisher : MDPI
Page : 510 pages
File Size : 53,8 Mb
Release : 2019-11-20
Category : Technology & Engineering
ISBN : 9783039216185

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Integral Transforms and Operational Calculus by H. M. Srivastava Pdf

Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications

Author : George A. Anastassiou,John Michael Rassias
Publisher : Springer Nature
Page : 746 pages
File Size : 47,5 Mb
Release : 2019-11-23
Category : Mathematics
ISBN : 9783030289508

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Frontiers in Functional Equations and Analytic Inequalities by George A. Anastassiou,John Michael Rassias Pdf

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers–Ulam stability of a discrete diamond–alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.

Author : Dumitru Bǎleanu,António Mendes Lopes
Publisher : Walter de Gruyter GmbH & Co KG
Page : 292 pages
File Size : 49,6 Mb
Release : 2019-04-01
Category : Mathematics
ISBN : 9783110571929

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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 eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.

Author : Bashir Ahmad,Johnny L Henderson,Rodica Luca
Publisher : World Scientific
Page : 468 pages
File Size : 50,9 Mb
Release : 2021-02-18
Category : Mathematics
ISBN : 9789811224478

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Boundary Value Problems For Fractional Differential Equations And Systems by Bashir Ahmad,Johnny L Henderson,Rodica Luca Pdf

This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.

Author : Carlo Cattani,Hari M. Srivastava,Xiao-Jun Yang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 392 pages
File Size : 43,8 Mb
Release : 2015-01-01
Category : Mathematics
ISBN : 9783110472097

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Fractional Dynamics by Carlo Cattani,Hari M. Srivastava,Xiao-Jun Yang Pdf

The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 51,5 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101

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Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf

This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Author : Bo Yang,Dusan Stipanovic
Publisher : BoD – Books on Demand
Page : 246 pages
File Size : 46,7 Mb
Release : 2023-03-15
Category : Mathematics
ISBN : 9781803569260

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Nonlinear Systems by Bo Yang,Dusan Stipanovic Pdf

In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of input. Nonlinear control systems, which are among the new technologies most widely used in many fields such as economic management, industrial production, technology research and development, ecological prevention and control, are at the core of worldwide automation control technology. In contrast to linear control systems, the nonlinear control system has the characteristics of a data model: stability, zero-input system response, self-excited oscillation or limit cycle, and a more complex structure, increasing the difficulty of its theoretical analysis and technical development. Nonlinear systems are common phenomena in real life and as such cannot be ignored. Analysis and research of nonlinear systems are therefore important, and researchers need to clarify their characteristics, explore scientific and effective application measures, and finally enhance their control quality. This book comprehensively investigates the main principles, core mechanisms, typical problems, and relevant solutions involved in nonlinear systems. In general, this book aims to provide advanced research on nonlinear systems and control schemes for researchers and engineers working in related fields, and thus promote future study in this research area.

Author : Snezhana Hristova
Publisher : MDPI
Page : 190 pages
File Size : 46,9 Mb
Release : 2021-02-22
Category : Mathematics
ISBN : 9783036500744

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Recent Investigations of Differential and Fractional Equations and Inclusions by Snezhana Hristova Pdf

During the past decades, the subject of calculus of integrals and derivatives of any arbitrary real or complex order has gained considerable popularity and impact. This is mainly due to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. In connection with this, great importance is attached to the publication of results that focus on recent and novel developments in the theory of any types of differential and fractional differential equation and inclusions, especially covering analytical and numerical research for such kinds of equations. This book is a compilation of articles from a Special Issue of Mathematics devoted to the topic of “Recent Investigations of Differential and Fractional Equations and Inclusions”. It contains some theoretical works and approximate methods in fractional differential equations and inclusions as well as fuzzy integrodifferential equations. Many of the papers were supported by the Bulgarian National Science Fund under Project KP-06-N32/7. Overall, the volume is an excellent witness of the relevance of the theory of fractional differential equations.

Author : Christopher Goodrich,Allan C. Peterson
Publisher : Springer
Page : 556 pages
File Size : 41,9 Mb
Release : 2016-02-09
Category : Mathematics
ISBN : 9783319255620

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Discrete Fractional Calculus by Christopher Goodrich,Allan C. Peterson Pdf

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject. Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1—2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers. For courses where students already have background in elementary real analysis, Chapters 1—2 may be covered quickly and readers may then skip to Chapters 6—7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6—7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1—5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.