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By using the notion of measure of non compactness, we will present in this work an extension of coupled fixed point theorem on banach ordered space and we will presente another results in metric space equipped with directed graph.

This paper provides common fixed point theorems for a commuting family of self mappings in Banach spaces via a measure of non-compactness. The choice of a commuting family of self maps provides a result that is unique in its own right, generalize Darbos fixed point theorem and specifically extend and improve the work of Meryeme El Harrak and Ahmed Hajji.

In this paper, we consider the fractional Langevin equation with finite delay. Our aim is to establish new conditions ensuring the existence, uniqueness and stability of solutions. This is realized...

In this work, we use the notion of convex power condensing mapping under measure of noncompactness in locally convex spaces and establish some new coupled fixed point results. The results proved herein are the generalization and extension of some widely known results in the existing literature. Furthermore, we apply our results for the existence of solution to infinite system of ordinary differential equations and system of fractional hybrid differential equations.

We study the solvability of a fractional Cauchy problem based on new development of fixed point theorem, where the operator is suggested to be non-compact on its domain. Moreover, we shall prove that the solution is bounded by a fractional entropy (entropy solution). For this purpose, we establish a collection of basic fixed point results, which generalizes and modifies some well known results. Our attention is toward the concept of a measure of non-compactness to generalize $\mu$-set contractive condition, using three control functions.

In this work, we prove the existence of solutions for a tripled systemof integral equations using some new results of fixed point theory associated withmeasure of noncompactness. These results extend the results in some previousworks. Also, the condition under which the operator admits fixed points is moregeneral than the others in literature.

We investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove existence results by applying Schauder's fixed point technique. Moreover, we show fundamental properties of the solution representation by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory., Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Fractal and Fractional' (ISSN 2504-3110), available at [https://www.mdpi.com/journal/fractalfract]. Submitted: 30-Dec-2020; Revised: 22-Feb-2021; Accepted to Fractal Fract: 4-March-2021

In this chapter, we use the concept of local fractional calculus and measure of non-compactness to design the growth system of Covid-19. To achieve this, we establish a fixed point and coupled fixed point theorems for new \(\mu \)-set contraction condition in partially ordered Banach spaces, whose positive cone \(\mathbb {K}\) is normal. We provide adequate examples to validate the epidemic dynamics with graphical presentations. We also use present available data to validate it.

In this paper, we extend Darbo&rsquo, s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

The aim of this work is to establish further existence of solution results for quantum stochastic differential equations with unbounded coefficients, which are also stochastic processes. Existence of solutions for nonlocal quantum stochastic differential equations with impulsive effects is established. The nonlocal condition extends the traditional initial value condition and cases of Lipschitz and non-Lipschitz continuous conditions were established. The quantum stochastic differential equation considered are driven by noises on Boson Fock spaces and measure of non compactness was employed to prove the main result.

In this paper, we prove the existence of decay integral solutions to a class of fractional differential inclusions with finite delays and estimate their decay rate. For these purposes, we have to construct a suitable regular measure of noncompactness on the space of solutions and then deploy the fixed point theory for condensing multivalued maps. An application to a class of fractional PDE with almost sectorial operator is also given.

This paper considers the fractional-order system in the sense of ψ -Hilfer fractional differential equations. In order to investigate the existence and uniqueness of the mild solution, the Banach contraction mapping principle and the measure of non-compactness are applied. As an application, the financial crisis model in the sense of ψ -Hilfer fractional differential equation will be used to prove the existence of solution and global stability of it. In addition, to illustrate the feasibility and validity of our results, the numerical simulation of the financial crisis model in the sense of Caputo will be shown in four different cases. Our results indicate that for non-integer order, the system behaves to be asymptotically stable and periodic (chaotic) at a certain limit order and the other part stabilizes to a fixed point.

We prove the global solvability and weakly asymptotic stability for a semilinear fractional differential inclusion subject to impulsive effects by analyzing behavior of its solutions on the half-line. Our analysis is based on a fixed point principle for condensing multi-valued maps, which is employed for solution operator acting on the space of piecewise continuous functions. The obtained results will be applied to a lattice fractional differential system.

We give a generalized version of the well-known Borsuk’s antipodal fixed point theorem for a large class of antipodally approachable condensing or compact set-valued maps defined on closed subsets of locally convex topological vector spaces. These results contain corresponding results obtained in the literature for compact set-valued maps with convex values.

У овој дисертацији су приказане неке нове особине извесних пресликавања контрактивног типа, и дате су примене тих резултата у нелинеарној анализи. Дисертација садржи шест поглавља. Прво поглавље садржи основне особине полу - метричких простора. У њој је дато и једно проширење Борел - Лебегове теореме за ту класу простора. У другом поглављу је доказано једно уопштење теореме о непокретној тачки Ниемитцког. У трећем поглављу је појам мере некомпактности проширен на класу полу – метричких простора. Такође је доказана теорема о фиксним тачкама за кондензујућа пресликавања дефинисана на тој класи простора. Следећа три поглавља садрже нове ставове о заједничким фиксним тачкама Мајр - Келеровог типа, нове резултате о акретивним пресликавањима и нове теореме о заједничким фиксним тачкама за пресликавања дефинисана на вероватносним метричким просторима. The aim of this dissertation is to present new properties of some classes of contractive mappings, and applications of this results to nonlinear analysis. It contain six chapters. The first chapter gives basic properties of semi-metric spaces. New result is extension of Borel - Lebesque theorem to semi metric spaces. The second chapter contain generalization of Niemytzki’s fixed point theorem. In third chapter the notion of measure of non-compactness are extended to class of semimetric spaces. New fixed point theorem for condensing mappings defined on semi-metric spaces is presented. Further three chapters contains new common fixed points theorems of Mair - Keeler type, new results for accretive mappings and new common fixed point results for mappings defined on probabilistic metric spaces.

We study the control systems governed by abstract Volterra equations without uniqueness in a Banach space. By using the technique of the theory of condensing maps and multivalued analysis tools, we obtain the existence result, investigate the topological structure of the solution set, and prove the invariance of a reachability set of the control system under nonlinear perturbations. Examples concerning fractional order differential equations and first order evolution equations with multiple delays are proposed to demonstrate the applications to approximate controllability results.

In this paper, using the technique of measure of noncompactness in Banach algebra, we prove an existence theorem for a nonlinear integral equation which contains as particular cases a lot of integral and functional-integral equations considered in nonlinear analysis and its applications. Our claim is also illustrated with the applications to some nonlinear functional-integral equation for proving the existence results.