Positive Solutions for Three-point Boundary Value Problem of Nonlinear Fractional q-difference Equation

Abstract

Abstract. In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

Positive Solutions for a Three-Point Boundary Value Problem of Fractional Q-Difference Equations

“…To solve these boundary value problems, some techniques have been applied, such as the monotone iterative technique, the lower-upper solution method, the Schauder fixed point theorem and the Krasnoselskii fixed point theorem. For details, one can see [13][14][15][19][20][21][22][23][24][25].…”

“…By using Schauder fixed point theorem and the Banach fixed point theorem, Yang [25] discussed a fractional q-difference equation with three-point boundary conditions:…”

Positive Solutions for Nonlinear Caputo Type Fractional q-Difference Equations with Integral Boundary Conditions

“…For some recent developments on fractional q-difference calculus and boundary value problems of fractional q-difference equations, see [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein. For example, authors [17][18][19][20] considered some anti-periodic boundary value problems of nonlinear fractional q-difference equations.…”