Fractional Differential Equations

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Lyapunov functions for fractional order systems

Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

Fixed Point Theory

In this survey paper, we shall establish sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problem for fractional differential equations and inclusions involving the Caputo fractional derivative. The both cases of convex and nonconvex valued right hand side are considered. The topological structure of the set of solutions is also considered.

A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions

Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index

Stability and Periodic Solutions of Ordinary and Functional Differential Equations

Preface. Preface to the second edition. Contents. 0 - Introduction and Overview 1 - The General Problems 2 - Linear Equations 3 - Existence Properties 4 - History, Examples and Motivation 5 - Instability, Stability and Perturbations 6 - Stability and Boundedness 7 - The Resolvent 8 - Functional Differential Equations References. Author Index. Subject Index.

Volterra integral and differential equations

You could buy lead Stability By Fixed Point Theory For Functional Differential Equations T A Burton or acquire it as soon as feasible. You could speedily download this Stability By Fixed Point Theory For Functional Differential Equations T A Burton after getting deal. So, as soon as you require the books swiftly, you can straight acquire it. Its correspondingly definitely simple and so fats, isnt it? You have to favor to in this appearance

Stability by Fixed Point Theory for Functional Differential Equations

A fixed-point theorem of Krasnoselskii

In this paper we focus on three fixed point theorems and an integral equation. Schaefer's fixed point theorem will yield a T-periodic solution of



(0.1) x(t)= a(t) + tt-h D(t,s)g(s,x(s))ds



if D and g satisfy certain sign conditions independent of their magnitude. A combination of the contraction mapping theorem and Schauder's theorem (known as Krasnoselskii's theorem) will yield a T-periodic solution of



(0.2) x(t) = f(t,x(t)) + tt-h D(t,s)g(s,x(s))ds



if f defines a contraction and if D and g are small enough.



We prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T-periodic solution of (0.2) when / defines a contraction mapping, while D and g satisfy the aforementioned sign conditions.

Theodore Burton

Papers

Stability and Periodic Solutions of Ordinary and Functional Differential Equations

Volterra integral and differential equations

Stability by Fixed Point Theory for Functional Differential Equations

A fixed-point theorem of Krasnoselskii

A Fixed Point Theorem of Krasnoselskii—Schaefer Type