Fixed Point Theory And Fractional Calculus

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Fixed Point Theory And Fractional Calculus

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Author : Pradip Debnath
language : en
Publisher: Springer Nature
Release Date : 2022-05-10

Fixed Point Theory And Fractional Calculus written by Pradip Debnath and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-10 with Mathematics categories.

This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.

Implicit Fractional Differential And Integral Equations

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Author : Saïd Abbas
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05

Implicit Fractional Differential And Integral Equations written by Saïd Abbas 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 2018-02-05 with Mathematics categories.

This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations

Advances In Functional Analysis And Fixed Point Theory

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Author : Bipan Hazarika
language : en
Publisher: Springer Nature
Release Date : 2024-04-22

Advances In Functional Analysis And Fixed Point Theory written by Bipan Hazarika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-22 with Mathematics categories.

This book presents a curated selection of recent research in functional analysis and fixed-point theory, exploring their applications in interdisciplinary fields. The primary objective is to establish a connection between the latest developments in functional analysis and fixed-point theory and the broader interdisciplinary research landscape. By doing so, this book aims to address the needs of researchers and experts seeking to stay up-to-date with the cutting-edge research trends in functional analysis, fixed-point theory and related areas. It also aims to pave the way for applying functional analysis and fixed-point theory to solve interdisciplinary problems in various domains, including but not limited to fractional calculus, integral equations, queuing theory, convex analysis, harmonic analysis and wavelet analysis.

Fractional Differential Equations

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Author : Anatoly Kochubei
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-02-19

Fractional Differential Equations written by Anatoly Kochubei 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 2019-02-19 with Mathematics categories.

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 second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.

Measure Of Noncompactness Fixed Point Theorems And Applications

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Author : S. A. Mohiuddine
language : en
Publisher: CRC Press
Release Date : 2024-04-24

Measure Of Noncompactness Fixed Point Theorems And Applications written by S. A. Mohiuddine and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with Mathematics categories.

The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem Discusses best proximity point results using measure of noncompactness and its applications Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.

Dynamical Systems

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Author : Mahmut Reyhanoglu
language : en
Publisher: BoD – Books on Demand
Release Date : 2017-03-15

Dynamical Systems written by Mahmut Reyhanoglu and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-15 with Mathematics categories.

There has been a considerable progress made during the recent past on mathematical techniques for studying dynamical systems that arise in science and engineering. This progress has been, to a large extent, due to our increasing ability to mathematically model physical processes and to analyze and solve them, both analytically and numerically. With its eleven chapters, this book brings together important contributions from renowned international researchers to provide an excellent survey of recent advances in dynamical systems theory and applications. The first section consists of seven chapters that focus on analytical techniques, while the next section is composed of four chapters that center on computational techniques.

Impulsive Differential Inclusions

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Author : John R. Graef
language : en
Publisher: Walter de Gruyter
Release Date : 2013-07-31

Impulsive Differential Inclusions written by John R. Graef and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-31 with Mathematics categories.

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Basic Theory Of Fractional Differential Equations Second Edition

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Author : Yong Zhou
language : en
Publisher: World Scientific
Release Date : 2016-10-20

Basic Theory Of Fractional Differential Equations Second Edition written by Yong Zhou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Mathematics categories.

This invaluable monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary and partial differential equations. It provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the technique of Picard operators, critical point theory and semigroup theory. Based on the research work carried out by the authors and other experts during the past seven years, the contents are very recent and comprehensive.In this edition, two new topics have been added, that is, fractional impulsive differential equations, and fractional partial differential equations including fractional Navier-Stokes equations and fractional diffusion equations.

Fixed Point Theory And Applications

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Author : Ravi P. Agarwal
language : en
Publisher: Cambridge University Press
Release Date : 2001-03-22

Fixed Point Theory And Applications written by Ravi P. Agarwal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-22 with Mathematics categories.

This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.

Measure Of Noncompactness Fixed Point Theorems And Applications

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Author : S. A. Mohiuddine
language : en
Publisher: CRC Press
Release Date : 2024-04-24

Measure Of Noncompactness Fixed Point Theorems And Applications written by S. A. Mohiuddine and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with Mathematics categories.

The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: • Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm • Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra • Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem • Discusses best proximity point results using measure of noncompactness and its applications • Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.