Krasnoselskii Fixed Point Theorem Research Articles

Existence of solutions to a class of nonlinear boundary value problems with right and left fractional derivarives

We discuss the existence of solutions for a boundary value problem involving both left Riemann-Liouville and right Caputo types derivatives. For this, we convert the posed problem to a sum of two integral operators then we apply Krasnoselskii's fixed point theorem to conclude the existence of nontrivial solutions.

Existence of solutions to discrete boundary value problem of fractional difference equations

In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the existence results.

Existence results for a semipositone singular fractional differential equation

This paper provides sufficient conditions to guarantee the existence and multiplicity of positive solutions for a singular semipositone fractional equation, subject to integral boundary value condition and parametric dependence $\mu $. Our approach relies on Krasnoselskii's fixed point theorem. Some examples are presented to illustrate our results.

Periodic solutions of a class of third-order differential equations with two delays depending on time and state

The goal of the present paper is to establish some new results on the existence, uniqueness and stability of periodic solutions for a class of third order functional differential equations with state and time-varying delays. By Krasnoselskii's fixed point theorem, we prove the existence of periodic solutions and under certain sufficient conditions, the Banach contraction principle ensures the uniqueness of this solution. The results obtained in this paper are illustrated by an example.

Existence results for fractional order boundary value problem with nonlocal non-separated type multi-point integral boundary conditions

In this article, we discuss the existence of solutions of a fractional boundary value problem of order m ∈ (1, 2], with nonlocal non-separated type integral multipoint boundary conditions. Shaefer type and Krasnoselskii's fixed point theorems are used to prove existence results for the given problem. To establish the uniqueness of solutions Banach contraction principle is used. The criteria for HyersUlam stability of the given boundary value problem is also discussed. Some examples are included for the illustration of our results.

On a coupled system of higher order nonlinear Caputo fractional differential equations with coupled Riemann\u2013Stieltjes type integro-multipoint boundary conditions

We study a coupled system of Caputo fractional differential equations with coupled non-conjugate Riemann–Stieltjes type integro-multipoint boundary conditions. Existence and uniqueness results for the given boundary value problem are obtained by applying the Leray–Schauder nonlinear alternative, the Krasnoselskii fixed point theorem and Banach’s contraction mapping principle. Examples are constructed to illustrate the obtained results.

Existence theory for nonlocal boundary value problems involving mixed fractional derivatives

In this paper, we develop the existence theory for a new kind of nonlocal three-point boundary value problems for differential equations and inclusions involving both left Caputo and right Riemann–Liouville fractional derivatives. The Banach and Krasnoselskii fixed point theorems and the Leray–Schauder nonlinear alternative are used to obtain the desired results for the singlevalued problem. The existence of solutions for the multivalued problem concerning the upper semicontinuous and Lipschitz cases is proved by applying nonlinear alternative for Kakutani maps and Covitz and Nadler fixed point theorem. Examples illustrating the main results are also presented.

FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND Ψ–HILFER FRACTIONAL DERIVATIVE

Considering a fractional integro-differential equation with nonlocal conditions involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem and Krasnoselskii's fixed point theorem. An example is provided to illustrate our main results.

Stability Results for Neutral Differential Equations by Krasnoselskii Fixed Point Theorem

In this paper we consider a neutral differential equation with variable delays and give some new conditions for the boundedness and stability results by using of Krasnoselskii’s fixed point theorem. Namely, a necessary and sufficient condition ensuring the asymptotic stability is proved, which improves and generalizes some results due to Burton and Furumochi (Dyn Syst Appl 11:499–519, 2002), and Jin and Luo (Nonlinear Anal 68:3307–3315, 2008). Finally, an example is exhibited to illustrate the effectiveness of the proposed results.

Existence and uniqueness of positive solutions for first-order nonlinear Liouville–Caputo fractional differential equations

We study the existence and uniqueness of positive solutions of the first-order nonlinear Liouville–Caputo fractional differential equation $$\begin{aligned} \left\{ \begin{array}{l} ^{C}D^{\alpha }\left( x\left( t\right) -g( t,x( t) ) \right) =f\left( t,x\left( t\right) \right) ,\quad 0 g\left( 0,x_{0}\right) >0, \end{array} \right. \end{aligned}$$where $$0<\alpha \le 1$$. In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ the Krasnoselskii fixed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach fixed point theorem to show the existence of a unique positive solution. Finally, an example is given to illustrate our results.

Asymptotic stability for mixed fractional delay differential equations

This paper is concerned with the stability analysis of nonlinear mixed fractional delay differential equations using Krasnoselskii's fixed point theorem in a weighted Banach space.

Positive Solutions for Systems of Fourth Order Two-Point Boundary Value Problems with Parameter

This paper deals with the existence of positive solutions for a system of nonlinear singular fourth-order differential equations with a parameter $\lambda$ subject two-point boundary conditions. Our analysis relies on the Krasnoselskii fixed point theorem and under suitable conditions, we derive explicit eigenvalue intervals of $\lambda$ for the existence of at least one positive solution for the system.

A Multidimensional Fixed-Point Theorem and Applications to Riemann-Liouville Fractional Differential Equations

In this work, we introduce a new version of Krasnoselskii fixed-point theorem dealing with N-tupled fixed-point results under certain blended conditions. Herein, we demonstrate that our newly theoretical results are applied to the investigation of Riemann-Liouville fractional differential equations (R-L FDEs for short). Furthermore, an example to illustrate the abstract results is obtained.

Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative

In this paper, the existence, uniqueness and stability of random implicit fractional differential equations (RIFDs) with nonlocal condition and impulsive effect involving a generalized Hilfer fractional derivative (HFD) are discussed. The arguments are discussed via Krasnoselskii's fixed point theorems, Schaefer's fixed point theorems, Banach contraction principle and Ulam type stability. Some examples are included to ensure the abstract results.

Existence results for fractional neutral integro-differential systems with nonlocal condition through resolvent operators

Abstract The manuscript is primarily concerned with the new existence results for fractional neutral integro-differential equation (FNIDE) with nonlocal conditions (NLCs) in Banach spaces. Based on the Banach contraction principle and Krasnoselskii fixed point theorem (FPT) joined with resolvent operators, we develop the main results. Ultimately, an representation is also offered to demonstrate the accomplished theorem.

Positive solutions of higher order fractional integral boundary value problem with a parameter

In this paper, we study a higher-order fractional differential equation with integral boundary conditions and a parameter. Under different conditions of nonlinearity, existence and nonexistence results for positive solutions are derived in terms of different intervals of parameter. Our approach relies on the Guo–Krasnoselskii fixed point theorem on cones.

$2p$ -th Moment Global Exponential Stability of a Unique $2P$ -th Mean Almost Periodic Oscillation for Semi-Discrete Takagi-Sugeno Fuzzy Stochastic Cellular Neural Networks With Time Delays

By using semi-discrete and Takagi-Sugeno fuzzy methods, a new version of discrete analogue of stochastic fuzzy cellular neural networks is formulated, which gives a more accurate characterization for continuous-time stochastic model than that by Euler scheme. Firstly, the 2p-th moment global exponential stability for the obtained semi-discrete stochastic Takagi-Sugeno fuzzy model is studied with the help of Minkowski inequality and Holder inequality. Secondly, the 2p-th mean almost periodic outputs of the model is investigated by using Krasnoselskii's fixed point theorem. Finally, illustrative examples and numerical simulations are given to demonstrate that our results are feasible.

Existence of positive periodic solutions for third-order nonlinear delay differential equations with variable coefficients

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x'''(t) + p(t)x''(t) + q(t)x'(t) + r(t)x(t) = f(t,x(t), x(t - t (t))) + d/dt g (t, x(t - t (t))), is considered. By employing Green's function and Krasnoselskii's fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order nonlinear delay differential equation.

Nonlinear Coupled Fractional Order Systems with Integro-Multistrip-Multipoint Boundary Conditions

We study the existence and uniqueness of solutions for a nonlinear system of coupled fractional differential equations equipped with nonlocal coupled integro-multistrip-multipoint boundary conditions. Our results are new in the sense that the given boundary conditions connect the values of the known functions over the given domain with the ones described on different sub-segments and different nonlocal positions within the given domain. We make use of Banach contraction mapping principle, Leray-Schauder alternative and Krasnoselskii fixed point theorem to prove the desired results for the problem at hand. An example illustrating the existence and uniqueness result is also presented.

Relative controllability of delay differential systems with impulses and linear parts defined by permutable matrices

This paper investigates the relative controllability of delay differential systems with linear impulses and linear parts defined by permutable matrices. We use the impulsive delay Grammian matrix to discuss the relatively controllability of impulsive linear delay controlled systems and we use the Krasnoselskii's fixed point theorem to discuss the relatively controllability of impulsive semilinear delay controlled systems. Finally, two examples are presented to illustrate our theoretical results.