Fixed point theorems in partially ordered Banach spaces with applications to nonlinear fractional evolution equations

Krasnoselskii N-Tupled Fixed Point Theorem with Applications to Fractional Nonlinear Dynamical System

“…, where is a nonempty set. In this paper, we extend the results of Yang et al [7] to prove a generalized version of N-tupled fixed point theorems. We give an application to the study existence of a solution of a system of nonlinear fractional differential evolution equations.…”

“…If is a nonempty subset of , is said to be a chain if each two elements , ∈ are comparable. We recall the following definitions which are given in [6,7].…”

“…The following theorem was given in [7] and will be used as a tool to prove the main results. Theorem 6.…”

“…More recently, in 2017, Yang et al [7] proved the Krasnoselskii coupled fixed point theorem under some or certain conditions and used their results to study the existence of the solution of a nonlinear coupled system of fractional differential equations. Imdad et al [8] in 2013, gave a new approach of the fixed point theory which was called N-tupled fixed point.…”

Several fixed point theorems on partially ordered Banach spaces and their applications to integral equations

“…Then, when we solve some problems on this Banach space, in addition to the topological structure and the algebraic structure, the ordering structure will provide a new powerful tool. This important idea has been widely used in solving integral equations ( [3][4][5], [7][8], [10], [11], [13]), vector variational inequalities ( [7]), nonlinear fractional evolution equations ( [14]), Nesh equilibrium problems ( [2], [6], [15]), etc.…”