This article is a survey, and its aim is to provide a concise introduction to the topic of measures of noncompactness and measures of weak noncompactness in Banach spaces. These measures constitute a useful tool in nonlinear analysis, for example, in...
We present a survey of the theory of measures of noncompactness and discuss some fixed point theorems of Darbo’s type. We apply the technique of measures of noncompactness to the characterization of classes of compact operators between certain...
In this paper, a tripled fractional differential system is introduced as three associated impulsive equations. The existence investigation of the solution is based on contraction principle and measures of noncompactness in terms of tripled fixed poin...
In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we d...
Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of Darbo’s fixed point theorem is given in this manuscript. Furthermore, some novel quadruple fixed points results via a measure of noncom...
Quadratic integro-differential equations have been discussed in many works, for instance. Some analytic results on the existence and the uniqueness of problem solutions to quadratic integro-differential equations have been investigated in different c...
In this paper, we prove some fixed point theorems for the nonlinear operator A · B + C in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the appl...
In the current contribution, an appropriate quantity connected to the space of all convergent sequences is provided and shown to be a measure of noncompactness in a Banach space. Through the application of the fixed point theorems of Darbo and Meir&n...
This article is devoted to the solvability and the asymptotic stability of a coupled system of a functional integral equation on the real half-axis. Our consideration is located in the space of bounded continuous functions on R+(BC(R+)). The main too...
In the current study, a new class of an infinite system of two distinct fractional orders with p-Laplacian operator is presented. Our mathematical model is introduced with the Caputo–Katugampola fractional derivative which is considered a generalizat...
The main goal of this study is to demonstrate an existence result of a coupled implicit Riemann-Liouville fractional integral equation. First, we prove a new fixed point theorem in spaces with an extended norm structure. That theorem generalized Darb...
In the present article, the Schauder-type fixed point theorem for the class of fuzzy continuous, as well as fuzzy compact operators is established in a fuzzy normed linear space (fnls) whose underlying t-norm is left-continuous at (1,1). In the fuzzy...
This paper introduces a new measure of non-compactness within a bounded domain of RN in the generalized Morrey space. This measure is used to establish the existence of solutions for a coupled Hadamard fractional system of integral equations in gener...
We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on...
This study demonstrates the total control of a class of hybrid neutral fractional evolution equations with non-instantaneous impulses and non-local conditions. The boundary value problem with non-local conditions is created using the Caputo fractiona...
In this manuscript, we establish the existence of results of fractional impulsive differential equations involving ψ-Hilfer fractional derivative and almost sectorial operators using Schauder fixed-point theorem. We discuss two cases, if the associat...
In this paper, we discuss some extensions of the Maligranda–Orlicz lemma. It deals with the problem of constructing a norm in a subspace of the space of bounded functions, for which it becomes a normed algebra so that the norm introduced is equ...
In this paper, we discuss the existence of solutions for a hybrid boundary value problem of Caputo fractional differential equations. The main tool used in our study is associated with the technique of measures of noncompactness. As an application, w...
The aim of this article is to establish the existence of the solution of non-linear functional integral equations x ( l , h ) = U ( l , h , x ( l , h ) ) + F l , h , ∫ 0 l ∫ 0 h P ( l , h , r , u , x ( r , u ) ) d r d...
In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Ba...
In the present paper, our main work aims to discover the existence result of the fractional order non-linear Hadamard functional integral equations on [1,a] by employing the theory of measure of non-compactness together with the fixed point theory in...
In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study...
In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed p...
In this article, we introduce several new extensions of Darbo’s fixed point theorem with newly constructed contraction functions associated with the measure of noncompactness. We apply our new extensions to prove the existence of solutions for...
In this work, we examine the existence of weak solution for a class of boundary value problems involving fractional Langevin inclusion with the Katugampola–Caputo fractional derivative under specified conditions contain the Pettis integrability...
This paper addresses some existence, attractivity and controllability results for semilinear integrodifferential equations having non-instantaneous impulsions on an infinite interval via resolvent operators in case of neutral and state-dependent dela...
We consider a non-instantaneous system represented by a second order nonlinear differential equation in a Banach space E. We use the family of linear bounded operators introduced by Kozak, Darbo fixed point method and Kuratowski measure of noncompact...
In this paper, we extend Darbo’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...
In this paper, we study a class of Caputo fractional q-difference inclusions in Banach spaces. We obtain some existence results by using the set-valued analysis, the measure of noncompactness, and the fixed point theory (Darbo and Mönch’s...
Here, we discuss the solvability of a class of hybrid functional integral equations by applying Darbo’s fixed point theorem and the technique of the measure of noncompactness (MNC). This study has been located in space BC (R+). Furthermore, we...
In this article, we examine the existence of Hilfer fractional (HF) stochastic differential systems with nonlocal conditions and delay via almost sectorial operators. The major methods depend on the semigroup of operators method and the Mo¨nch fi...
The aim of this article is to introduce and study a new class of fractional integro nonlocal boundary value problems involving the p-Laplacian operator and generalized fractional derivatives. The existence of solutions in Banach spaces is investigate...
In this paper, we establish sufficient conditions for the existence of mild solutions for certain impulsive evolution differential equations with causal operators in separable Banach spaces. We rely on the existence of mild solutions for the strongly...
In the present paper, the concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo fractional derivative. New results on the existence and uniqueness are established by using the theory of opera...
In this theory, the existence of a mild solution for a neutral partial integrodifferential nonlocal system with finite delay is presented and proved using the techniques of the Monch–Krasnosel’skii type of fixed point theorem, a measure o...
The goal of this paper is to study the existence of a mild solution and controllability for a class of neutral stochastic differential equations (SDEs) involving the Ψ-Hilfer fractional derivatives, a generalization of the well-known Riemann&ndas...
In this paper, by using the cosine family theory, measure of non-compactness, the Mönch fixed point theorem and the method of estimate step by step, we establish the existence theorems of mild solutions for fractional impulsive integro-different...
This manuscript mainly focuses on the exact controllability of Sobolev-type Hilfer fractional neutral delay Volterra-Fredholm integro-differential systems. The principal findings of this discussion are established by using the theories on fractional...
The purpose of the paper is to establish a sufficient condition for the existence of a solution to the equation T(u,C(u))=u using Kannan-type equicontractive mappings, T:A×C(A)¯→Y, where C is a compact mapping, A is a bounded, closed...
A boundary value problem for Hadamard fractional differential equations of variable order is studied. Note the symmetry of a transformation of a system of differential equations is connected with the locally solvability which is the same as the exist...
In this research paper, we investigate the controllability in the α-norm of a coupled system of integrodifferential equations with state-dependent nonlocal conditions in generalized Banach spaces. We establish sufficient conditions for the syst...
The current study demonstrates the existence of solutions to a multidimensional functional integral equation with multivalued feedback. We seek solutions for the multidimensional functional problem that is defined, continuous, and bounded on the semi...
This manuscript mainly focused on the nonlocal controllability of Hilfer fractional stochastic differential equations via almost sectorial operators. The key ideas of the study are illustrated by using ideas from fractional calculus, the fixed point...
Existence of the solution for the nonlinear quadratic integral equation of the Hammerstein type in the Banach space BC(R+) has been proved by using the technique of measure of noncompactness and fixed-point theorem. In this article, we obtain an appr...
In this paper, we investigate the existence of mild solutions to a multi-term fractional integro-differential equation with random effects. Our results are mainly relied upon stochastic analysis, Mönch’s fixed point theorem combined with a random fix...
We provide and prove some new fundamental properties of the Erdélyi–Kober (EK) fractional operator, including monotonicity, boundedness, acting, and continuity in both Lebesgue spaces (Lp) and Orlicz spaces (Lφ). We employ these prop...
We give a new and simplified definition of spectrumfor a nonlinear operator F acting in a real Banach space X, and study some of its features in terms of (qualitative and) quantitative properties of F such as the measure of noncompactness, &alpha...
The authors investigate the existence of solutions to a class of boundary value problems for fractional q-difference equations in a Banach space that involves a q-derivative of the Caputo type and nonlinear integral boundary conditions. Their result...
In this paper, we present some results of coupled fixed points for the system of non-linear integral equations in Banach space. Our results enlarge the results of newer papers. Additionally, we prove the applicability of those results to the solvabil...
In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on...
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