Fixed-Point Theorems for Systems of Operator Equations and Their Applications to the Fractional Differential Equations

Abstract

We study the existence and uniqueness of positive solution for a class of nonlinear binary operator equations systems by means of the cone theory and monotone iterative technique, under more general conditions. Also, we give the iterative sequence of the solution and the error estimation of the system. Moreover, we use this new result to study the existence and uniqueness of the solutions for fractional differential equations systems involving integral boundary value conditions in ordered Banach spaces as an application. The results obtained in this paper are more general than many previous results and complement them.

Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities

“…Coupled systems of fractional-order differential equations have also been investigated by many authors (see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][25][26][27][28][29][30][31][32][33][34][35][36] and the references therein). In [7], the authors used coincidence degree theory to establish an existence result for a coupled system of nonlinear fractional differential equations:…”

Positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions

“…γ ,δ η is a Erdélyi-Kober type integral, and ρ I p denotes the generalized Riemann-Liouville type integral boundary conditions. For fractional differential systems, see [23][24][25][26][27][28][29][30][31][32]. In [23], using the Leray-Schauder alternative and the Banach contraction principle, the authors studied existence and uniqueness of solutions for the system of nonlinear Caputo type sequential fractional integro-differential equations…”

Analysis of coupled systems of implicit impulsive fractional differential equations involving Hadamard derivatives

“…Such systems appear naturally in many real-world situations. Some recent results on the topic can be found in a series of papers [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] and the references cited therein.…”