By using Krasnoselskii’s fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problem Δ2u t − 1 a t f u t 0, t ∈ {1, 2, . . . , T}, u 0 β ∑η s 1 u s , u T 1 α ∑η s 1 u s , where f is continuous, T ≥ 3 is a fixed positive integer, η ∈ {1, 2, ..., T − 1}, 0 < α < 2T 2 /η η 1 , 0 < β < 2T 2 − αη η 1 /η 2T − η 1 , and Δu t − 1 u t − u t − 1 ....

Abstract. In this work, by virtue of the Krasnoselskii–Zabreiko fixed point theorem, we investigate the existence of positive solutions for a class of fractional boundary value problems under some appropriate conditions concerning the first eigenvalue of the relevant linear operator. Moreover, we utilize the method of lower and upper solutions to discuss the unique positive solution when the no...

In this paper, we first study a hierarchical problem of Baillon’s type, and we study a strong convergence theorem of this problem. For the special case of this convergence theorem, we obtain a strong convergence theorem for the ergodic theorem of Baillon’s type. Our result of the ergodic theorem of Baillon’s type improves and generalizes many existence theorems of this type of problem. Two nume...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

This paper studies the existence of solutions for a coupled system of nonlinear fractional differential equations. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.

in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.