Positive solutions for a class of fractional difference systems with coupled boundary conditions

Abstract

In this paper we use the fixed point index and nonnegative matrices to study the existence of positive solutions for a class of fractional difference systems with coupled boundary conditions.

Variational Methods for an Impulsive Fractional Differential Equations with Derivative Term

“…In particular, the solvability, attractivity, and multiplicity of solutions for FDEs have been greatly discussed. We refer to the monographs of Podlubny [1], Kilbas et al [2], Diethelm [3], Zhou [4], the papers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein.…”

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

“…Moreover, if there is a y ∈ P, a fixed point of A, and y(t) ≥ w(t), t ∈ [1, e], then we have that y(t) − w(t) is a positive solution of (18). From (12) and (18), we have (12). erefore, in what follows, we study the existence of fixed points of the operator A, which are greater than w. □ Lemma 4.…”

“…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:…”

Iterative Solution for Systems of a Class of Abstract Operator Equations in Banach Spaces and Application

“…Suppose that for n � k, one has (12) and (13). en, as n � k + 1, by (2) and (3), the following is obtained:…”