Positive Solutions for Boundary Value Problem of Nonlinear Fractional -Difference Equation

Abstract

We investigate the existence of multiple positive solutions to the nonlinear q-fractional boundary value problem c D a q u t a t f u t 0, 00, by using a fixed point theorem in a cone.

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

“…Ma and Yang [26] considered the existence of solutions for multi-point boundary value problems of nonlinear fractional q-difference equations by means of the Banach contraction principle and Krasnoselskii's fixed point theorem. 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.…”

Positive Solutions for Singular Boundary Value Problem with Fractional $$q$$ q -Differences

“…Recently, there are few works consider the existence of positive solutions for nonlinear q-fractional boundary value problem (see [8,13,28,29]). As is well-known, the aim of finding positive solutions to boundary value problems is of main importance in various fields of applied mathematics (see the book [30] and references therein).…”

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

“…There have been some papers dealing with the existence and multiplicity of solutions or positive solutions for boundary value problems involving nonlinear fractional q-difference equations, such as the Krasnosel'skii fixed-point theorem, the Leggett-Williams fixed-point theorem, and the Schauder fixed-point theorem, For examples, see [8,9] and the references therein.…”