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This study concerns a Krasnoselskii-type fixed point theorem for the sum of two operators A,BA,B in a Banach space EE, where BB is a Reich-type contractive mapping and AA is a k-set contractive mapping. We introduce a class of operators θ:X×X→[1,+∞)\theta :X\times X\to \left[1,+\infty ) satisfying some axioms and use it as a new metric to prove a fixed point theorem in the spirit of Azam et al. [Reich-Krasnoselskii-type fixed point results with applications in integral equations, J. Inequal. Appl. 2023 (2023), 131].

The present work examines the solvability of a tripled system of fractional Langevin differential equations with cyclic antiperiodic boundary conditions. The Krasnoselskii fixed point theorem, the Banach contraction mapping theorem, and specific properties of the Mittag-Leffler functions are employed to establish sufficient conditions for the existence and uniqueness of solutions. The feasibility of the primary findings is illustrated through the discussion of several numerical examples. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we construct the fixed point index for a class of contractive mapping defined by a simulation mapping and a measure of noncompact-ness noted by Zµ− contraction maps. Then we establish some fixed point theorem for this mapping of the Krasnoselskii type. An Application to the integral equation is presented to support the results.

This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 < \theta < 1 $ in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an $ \theta $-resolvent family. Then we study the existence of this mild solution by using Krasnoselskii's fixed point theorem. Finally, we give an example to prove our results.

This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order 0 < θ < 1 in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an θ-resolvent family. Then we study the existence of this mild solution by using Krasnoselskii’s fixed point theorem. Finally, we give an example to prove our results. [ABSTRACT FROM AUTHOR]

In order to extend the basic theory of boundary value problems, the existence of solutions for a class of Hilfer fractional impulsive differential equations with finite impulsive points was studied. Firstly, the integral equation equivalent to the differential equation was obtained; Secondly, appropriate Banach spaces and norms were defined, and appropriate operators were constructed. When the nonlinear term satisfies different conditions, sufficient conditions for the existence of solutions of such boundary value problems were obtained by using Krasnoselskii fixed point theorem; Finally, two examples were used to illustrate the universality of the research results. It is shown that the solution of the boundary value problem of impulsive differential equations with Hilfer fractional derivative exists. By using the Krasnoselskii fixed-point theorem, the existence of solutions for impulsive differential equation boundary value problems with Hilfer fractional order can be effectively solved, which provides some reference for solving other types of impulsive fractional differential equation boundary value problems.

Symmetry is presented in many works involving differential and integral equations. Whenever a human is involved in the design of an integral equation, they naturally tend to opt for symmetric features. The most common examples are the Green functions and linguistic kernels that are often designed symmetrically and regularly distributed over the universe of discourse. In the current study, the authors report a study on boundary value problem (BVP) for a nonlinear integro Volterra–Fredholm integral equation with variable coefficients and show the existence of solution by applying some fixed-point theorems. The authors employ various numerical common approaches as the homotopy analysis methodology established by Liao and the modified Adomain decomposition technique to produce a numerical approximate solution, then graphical depiction reveals that both methods are most effective and convenient. In this regard, the authors address the requirements that ensure the existence and uniqueness of the solution for various variations of nonlinearity power. The authors also show numerical examples of how to apply our primary theorems and test the convergence and validity of our suggested approach. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Hebei University of Science & Technology is the property of Hebei University of Science & Technology, Journal of Hebei University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Two main results of fixed point theory in infinite dimensional space are Schauder's theorem and the contraction mapping principle. Krasnoselskii combined them into one fixed point result. In this paper, we continue the study of extensions of these theorems investigating a convex modular in a original vector space, not in modular space and without Δ 2 condition, to provide certain extensions of Banach contraction principle and Krasnoselskii fixed point theorem. We applied that theorem to solve the nonlinear periodic problem of Hill's equation. [ABSTRACT FROM AUTHOR]

In this paper, we present some results concerning the existence and attractivity of solutions for generalized Cauchy problem involving Hilfer fractional derivative using the well-known Krasnoselskii fixed point theorem and the measure of noncompactness. Finally, some examples are provided to illustrate the efficiency of the results. [ABSTRACT FROM AUTHOR]

In this article, we consider a nonlinear neutral q-fractional difference equation. So, we apply the fixed point theorem of Krasnoselskii to obtain the existence of solutions under sufficient conditions. After that, we use the fixed point theorem of Banach to show the uniqueness, as well as the stability of solutions. Our main results extend and generalize previous results mentioned in the conclusion. [ABSTRACT FROM AUTHOR]

This paper studies Langevin equation with nonlocal boundary conditions involving a ψ-Caputo fractional operators of different orders. By the aid of fixed point techniques of Krasnoselskii and Banach, we derive new results on existence and uniqueness of the problem at hand. Further, a new ψ-fractional Gronwall inequality and ψ-fractional integration by parts are employed to prove Ulam-Hyers and Ulam-Hyers-Rassias stability for the solutions. Examples are provided to demonstrate the advantage of our major results. The proposed results here are more general than the existing results in the literature which can be obtained as particular cases.

This paper is concerned with the controllability of a nonlinear impulsive fractional integro-differential nonlocal control system with state-dependent delay in a Banach space. At first, we introduce a mild solution for the control system by using fractional calculus and probability density function. Under sufficient conditions, the results are obtained by means of semigroup theory and the Krasnoselskii fixed point theorem. Finally, an example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

Abstract Some essential conditions for existence theory and stability analysis to a class of boundary value problems of fractional delay differential equations involving Atangana–Baleanu-Caputo derivative are established. The deserted results are derived by using the Banach contraction and Krasnoselskii’s fixed point theorems. Moreover, different kinds of stability theory including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam-Rassias and generalized Hyers–Ulam–Rassias stability are also developed for the problem under consideration. Appropriate examples are given for illustrative purposes.

Abstract In this paper, by means of the Krasnoselskii fixed point theorem, the existence of solutions for a boundary value problem of nonlinear sequential fractional integro-differential equations are investigated. Two examples are given to illustrate our results.

In this paper, we prove the existence of solution of two nonlinear integral inclusions by using generalization of Krasnoselskii fixed point theorem for set-valued mappings. As an application we prove the existence of solution of the boundary valued problem of ordinary differential inclusion. [ABSTRACT FROM AUTHOR]

The goal of this paper is to consider a new fuzzy differential system consisting of a fuzzy fractional differential inclusion combined with a variational inequality, which is called fuzzy fractional differential variational inequality (FFDVI). Such a model captures the desired features of both fuzzy fractional differential inclusions and fractional differential variational inequalities within the same framework. By employing the set-valued version of the Krasnoselskii fixed point theorem, an existence of solutions is obtained for the FFDVI under some mild conditions. Moreover, an approximating algorithm is provided to find a solution of the FFDVI. Finally, two numerical examples are given to illustrate our main results. [ABSTRACT FROM AUTHOR]

The main aim of this article is to investigate some new sufficient conditions of the existence and uniqueness results of ψ -Hilfer fractional functional differential equations with nonlocal condition and finite delay. Further, Ulam–Hyers–Mittag-Leffler stability of solutions to a proposed problem is discussed. Krasnoselskii fixed point theorem, Picard operator method and Gronwall's inequality lemma are the main tools of our analysis. An illustrative example is provided in support of the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear neutral fractional difference equations. By applying Krasnoselskii's fixed point theorem, sufficient conditions for the existence of solutions are established. Also, the uniqueness of a solution is given. As an application of the main theorems, we provide the existence and uniqueness of the discrete fractional Lotka-Volterra model of neutral type. Our main results extend and generalize the results that are obtained in [6]. [ABSTRACT FROM AUTHOR]

In this paper, by means of the Krasnoselskii fixed point theorem, the existence of solutions for a boundary value problem of nonlinear sequential fractional integro-differential equations are investigated. Two examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

Some essential conditions for existence theory and stability analysis to a class of boundary value problems of fractional delay differential equations involving Atangana–Baleanu-Caputo derivative are established. The deserted results are derived by using the Banach contraction and Krasnoselskii's fixed point theorems. Moreover, different kinds of stability theory including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam-Rassias and generalized Hyers–Ulam–Rassias stability are also developed for the problem under consideration. Appropriate examples are given for illustrative purposes. [ABSTRACT FROM AUTHOR]

In the current paper, we have studied fractional order differential equation containing Atangana-Baleanu fractional derivative in the sense of Caputo. We have studied the existence of the solution of the concerned problem with the help of using the tools of fixed point theory. Apart from this the authors have investigated the uniqueness of the solution as well. With all these we have also analysed the stability of the solution for which we have used the Ulam-Hyer’s and generalized Ulam stability. We have derived all the conditions for the aforementioned work. To validate the results we derived have been illustrated through the given examples. For the existence of the solution the authors have utilized Banach and Krasnoselskii’s theorems. [ABSTRACT FROM AUTHOR]

The aim of this article is to study approximate controllability of a class of non-autonomous Sobolev type integro-differential equations having non-instantaneous impulses with nonlocal initial condition. The results will be proved with the help of evolution system and Krasnoselskii fixed point theorem. An example is presented to show how our abstract results can be applied. [ABSTRACT FROM AUTHOR]

Using Krasnoselskii’s fixed point theorem and Arzela–Ascoli theorem, we investigate the existence of solutions for a system of nonlinear ϕ-Hilfer fractional differential equations. Moreover, applying an alternative fixed point theorem due to Diaz and Margolis, we prove the Kummer stability of the system on the compact domains. We also apply our main results to study the existence and Kummer stability of Lotka–Volterra’s equations that are useful to describe and characterize the dynamics of biological systems.

The aim of this article is to investigate the existence of mild solutions as well as approximate controllability of non-autonomous Sobolev type differential equations with the nonlocal condition. To prove our results, we will take the help of Krasnoselskii fixed point technique, evolution system and controllability of the corresponding linear system.

In this study, we aim to present some new versions of classical Schauder and Banach fixed point theorems under weak topology in general Banach spaces. We have also another main goal which is to prove that Krasnoselskii theorem ensures in general Banach spaces using these new results. As an application, an illustrative example providing such results is given. Our results extend known results on the issue. [ABSTRACT FROM AUTHOR]

In this article, some existence and uniqueness of solutions for a new class of global fractional-order projective dynamical system with delay and perturbation are proved by employing the Krasnoselskii fixed point theorem and the Banach fixed point theorem. Moreover, an approximating algorithm is also provided to find a solution of the global fractional-order projective dynamical system. Finally, an application to the idealized traveler information systems for day-to-day adjustments processes and a numerical example are given. [ABSTRACT FROM AUTHOR]

The aim of this article is to investigate the existence of mild solutions as well as approximate controllability of non-autonomous Sobolev type differential equations with the nonlocal condition. To prove our results, we will take the help of Krasnoselskii fixed point technique, evolution system and controllability of the corresponding linear system. [ABSTRACT FROM AUTHOR]

IN this paper, we consider a class of nonlinear fractional integro-differential equations with fractional derivative of Capturo sense. We shall rely on the Krasnoselskii fixed point theorem to obtain the ex-istence result in Banach spaces, Moreover, one of Krasnoselskii-Krein conditions is applied to establish the result. Finally, an illustrative example is also presented. [ABSTRACT FROM AUTHOR]

The existence and uniqueness of solutions for nonlinear delay fractional difference equations are investigated in this paper. We prove the main results by employing the theorems of Krasnoselskii's Fixed Point and Arzela-Ascoli. As an application of the main theorem, we provide an existence result on the discrete fractional Lotka-Volterra model. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of nonlinear fractional differential equations on the infinite interval [ABSTRACT FROM AUTHOR]

We study the existence of solutions of the functional quadratic integral equation with a perturbation term in the space of Lebesgue integrable functions on an unbounded interval by using the Krasnoselskii fixed point theory and the measure of weak noncompactness.

This article concerns the solvability of the higher-order nonlinear neutral delay difference equation $$ DeltaBig(a_{kn}dotsDeltaig(a_{2n} Delta(a_{1n}Delta(x_n+b_nx_{n-d}))ig)Big) +sum_{j=1}^s p_{jn}f_j(x_{n-r_{jn}})=q_n, $$ where $ngeq n_0ge0$, $d,k,j,s$ are positive integers, $f_j:mathbb{R}o mathbb{R}$ and $xf_j(x)geq 0$ for $x e 0$. Sufficient conditions for the existence of non-oscillatory solutions are established by using Krasnoselskii fixed point theorem. Five theorems are stated according to the range of the sequence ${b_n}$.

We are interested in the existence of positive solutions to a four-point boundary value problem of the differential equation $ y''(t) + a(t)f(y(t))=0 $ on $ [0,1] $. The value of $y$ at $0$ and $1$ are each a multiple of $y(t)$ at an interior point. Many known existence criteria are based on the limiting values of $ f(u)/u $ as $u$ approaches $0$ and infinity.

In this paper, by using the Schauder fixed point theorem, Krasnoselskii fixed point theorem and some new techniques, we obtain the existence of uncountably many solutions for a third order nonlinear difference equation with neutral delay of the form Δ(a(n, xa1n, xa2n, …, xarn)Δ2(xn + bnxn-r)) + Δh(n, xh1n, xh2n, …, xhkn) + f(n, xf1n, xf2n, …, xfkn) = cn, n ≥ n0. The results presented improve and generalize some results in literatures. Seven examples are given to illustrate the results presented in this paper. [ABSTRACT FROM AUTHOR]

In this article, we investigate the existence of positive periodic solutions for a class of non-autonomous difference equations. Using the Krasnoselskii fixed point theorem, we establish sufficient criteria that are easily verifiable and that generalize and improve related studies in the literature. Numerical simulations are presented which support our theoretical results for some concrete models.

In this paper, sufficient criteria are established for the existence of periodic solutions of a class of functional dynamic equations with impulses on time scales. The systems under consideration are general enough to incorporate many mathematical models arising in ecological equations. The approach is mainly based on the Krasnoselskii fixed point theorem, which has been extensively applied to the study of existence problem. [ABSTRACT FROM AUTHOR]

In this paper, we employ the well-known Krasnoselskii fixed point theorem to study the existence and n-multiplicity of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. The form including an impulsive term of the equations in this paper is rather general and incorporates as special cases various problems which have been studied extensively in the literature. Easily verifiable sufficient criteria are obtained for the existence and n-multiplicity of positive periodic solutions of the impulsive functional differential equations. [ABSTRACT FROM AUTHOR]

We study the existence of solutions of the functional quadratic integral equation with a perturbation term in the space of Lebesgue integrable functions on an unbounded interval by using the Krasnoselskii fixed point theory and the measure of weak noncompactness. [ABSTRACT FROM AUTHOR]

In this paper, we study fixed point theorems and new variants of some nonlinear altenatives of Krasnoselskii type in Banach spaces by using measures of weak noncompactness. Then we give an application to solve a nonlinear Hammerstein integral equation in L1 spaces. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper is to study the existence and uniqueness of fixed point for a class of nonlinear mappings defined on a real Banach space, which, among others, contains the class of separate contractive mappings, as well as to see that an important class of 1-set contractions and of pseudocontractions falls into this type of nonlinear mappings. As a particular case, we give an iterative method to approach the fixed point of a nonexpansive mapping. Later on, we establish some fixed point results of Krasnoselskii type for the sum of two nonlinear mappings where one of them is either a 1-set contraction or a pseudocontraction and the another one is completely continuous, which extend or complete previous results. In the last section, we apply such results to study the existence of solutions to a nonlinear integral equation. [Copyright &y& Elsevier]

Abstract: This paper deals with the study of existence of solutions of nonlinear fractional integrodifferential equations of Sobolev type with nonlocal condition in Banach spaces. The results are obtained by using resolvent operators, fractional calculus and fixed point technique. An example is provided to illustrate the theory. [Copyright &y& Elsevier]

In this paper, using the well-known Krasnoselskii fixed point theorem, we obtain the existence of a square-mean almost periodic solution to some classes of nonautonomous stochastic evolution equations with finite delay. [ABSTRACT FROM AUTHOR]

Abstract: By using Krasnoselskii’s fixed point theorem, we obtain a sufficient condition for the existence of positive periodic solutions for the delay Nicholson’s blowflies model with a harvesting term. Three examples and numerical simulation are given to illustrate the effectiveness of our result. [Copyright &y& Elsevier]

Abstract: In this paper, we will give conditions which will guarantee the existence of positive solutions for a variety of second order boundary value problems, using the well-known Krasnoselskii fixed point theorem. We will deal with a specific differential equation meeting a specific initial condition and use a general boundary condition, involving a not necessarily linear functional. Our purpose is to pose conditions on that functional, which will guarantee that the Krasnoselskii fixed point theorem can be applied. It is important to notice that only the values of this functional on two specific functions are involved in the conditions we pose. This paper unifies the way we deal with a wide variety of boundary value problems and provides results which, to the best of our knowledge, are new. [Copyright &y& Elsevier]

Abstract: We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results. [Copyright &y& Elsevier]