Existence results for fractional q-difference equations with nonlocal q-integral boundary conditions

Abstract

In this paper, we discuss the existence of positive solutions for nonlocal q-integral boundary value problems of fractional q-difference equations. By applying the generalized Banach contraction principle, the monotone iterative method, and Krasnoselskii's fixed point theorem, some existence results of positive solutions are obtained. In addition, some examples to illustrate our results are given.

Positive solutions for nonlinear semipositone fractional q-difference system with coupled integral boundary conditions

“…El-Shahed and Al-Askar [20] studied the existence of multiple positive solutions to the nonlinear q-fractional boundary value problems by using GuoKrasnoselskii's fixed point theorem in a cone. Zhao et al [30] showed some existence results of positive solutions to nonlocal q-integral boundary value problem of nonlinear fractional q-derivatives equation using the generalized Banach contraction principle, the monotone iterative method, and Krasnoselskii's fixed point theorem.…”

Infinitely many solutions for fractional differential system via variational method

“…For details, see [1][2][3]. Recently, a great deal of work has been done in the study of the existence and uniqueness of solutions to nonlinear fractional differential equations (see [1][2][3][4][5][6][7][8][9][10][31][32][33] and the references therein). Some classical tools have been used to investigate such problems in the literature, such as some fixed point theorems in cones, the coincidence degree theory of Mawhin, and the method of upper and lower solutions with the monotone iterative technique.…”

On Riemann‐Liouville fractional q–difference equations and their application to retarded logistic type model

“…The methods used to prove existence theorems are based on Krasnoselskii fixed-point theorem, the lower and upper solution method, the critical point theory, and fixed-point theorem on cones. [16][17][18][19][20][21][22][23][24][25] However, most of the above-mentioned papers have studied the boundary value problems within Caputo fractional operators. The initial value problems involving fractional q-difference equations defined via Riemann-Liouville settings have rarely been under investigation.…”