We discuss the existence of solutions for second-order impulsive differential equation with nonlocal conditions in Banach spaces. Our approach is based on generalization Schauder fixed pointprinciple that Darbo point theorem. An example also presented to illustration.

This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.

In this work, we present some results on the existence of attractive solutions fractional differential equations ѱ-Hilfer hybrid type. The are a consequence Schauder fixed point theorem. Next, prove that all uniformly locally attractive.

In this paper, we study the existence of solution to integro-differential equations in space Lebesgue-integrable on un-bounded interval after transformed nonlinear integral functional equation, used tool is fixed point theorem due Schauder with weak measure non compactness, De-Blasi. addition, give an example which satisfies conditions our theorem.

The solution to a sequential fractional differential equation with affine periodic boundary value conditions is investigated in this paper. existence theorem of established by means the Leray–Schauder fixed point and Krasnoselskii theorem. What more, uniqueness demonstrated via Banach contraction mapping principle. In order illustrate main results, two examples are listed.

*Correspondence: [email protected] Department of Mathematics, Eastern Mediterranean University, Gazimagusa, Turkish Republic of Northern Cyprus Abstract In this paper, we study existence (uniqueness) of solutions for nonlinear fractional differential equations with Katugampola fractional integral conditions. Several fixed point theorems are used for sufficient conditions of existence (u...

Abstract: In this paper, we establish some sufficient conditions for the existence and nonexstence of positive solutions to a general class of higher-order nonlinear fractional differential equation. The results are established by converting the problem into an equivalent integral equation and applying Banach fixed point theorem, nonlinear differentiation of Leray-Schauder type and the fixed po...

and Applied Analysis 3 Definition 2.2. For f, g ∈ E the order interval 〈f, g〉 is defined as 17 〈 f, g 〉 { h ∈ E : f ≤ h ≤ g. 2.1 Definition 2.3. A subset E ⊂ Π is called order bounded if E is contained in some order interval. Definition 2.4. A coneK is called normal if there exists a positive constant μ such that f, g ∈ V and θ ≺ f ≺ g implies that ‖f‖ ≤ μ‖g‖. We state the two fixed point resul...

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinear qdifference equations with three-point q-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach’s contraction mapping, Krasnoselskii’s fixed-point theorem, and Leray-Schauder degree theory, some ...

In this paper, we investigate the existence of positive solutions for second-order nonlinear three-point integral boundary value problems. By using the Leray-Schauder fixed point theorem, some sufficient conditions for the existence of positive solutions are obtained, which improve the results of literature Tariboon and Sitthiwirattham [J. Tariboon, T. Sitthiwirattham, Boundary Value Problems, ...