Erdal Karapinar - Böcker

This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics.

This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics.

This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers’ understanding of the concepts presented.Includes illustrations in order to support readers understanding of the presented concepts·         Approaches the topic of fractional differential equations while employing fixed point theorems as tools·         Presents novel results, which build upon previous literature and many years of research by the authors

This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers’ understanding of the concepts presented.Includes illustrations in order to support readers understanding of the presented concepts·         Approaches the topic of fractional differential equations while employing fixed point theorems as tools·         Presents novel results, which build upon previous literature and many years of research by the authors

This book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives.

This book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives.

This book offers a unified and rigorous treatment of nonlinear differential equations involving the Caputo tempered fractional derivative and its generalizations. Spanning nine chapters, the authors systematically develop analytical methods for solving a wide variety of problems, including those with nonlocal, impulsive, periodic and delayed structures, within both deterministic and random settings. Each chapter is dedicated to a particular class of problems, beginning with global convergence and uniqueness analysis for the successive approximations method and extending to systems with neutral and infinite delays, boundary value problems with impulses, and coupled systems. The analytical approaches employed throughout the book include a rich array of mathematical tools: fixed point theory (Banach, Schauder, Darbo, Monch, Schaefer, Sadovskii, and Krasnoselskii); coincidence degree theory; the method of upper and lower solutions; diagonalization techniques; and the measure of noncompactness. Special attention is given to various notions of stability, including Ulam-Hyers and Mittag-Leffler-Ulam-Hyers stability, as well as the existence of periodic and weak solutions. To ensure practical relevance and illustrate the applicability of each theoretical result, every chapter concludes with a section devoted to remarks and bibliographical suggestions as well as examples that highlight the effectiveness of the proposed methods. This book is ideal for graduate students, researchers, and professionals working in the fields of applied mathematics, differential equations, and fractional calculus.

Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology.The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework.Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise naturally in applications. As a result, fixed point theory is an important area of study in pure and applied mathematics and it is a flourishing area of research.