Abstract
In this paper, we consider the boundary value problem of a class of nonlinear fractional q-difference equations involving the Riemann–Liouville fractional q-derivative on the half-line. By means of Schauder fixed point theorem and Leggett–Williams fixed point theorem, some results on existence and multiplicity of solutions are obtained.
Highlights
Quantum calculus, roughly speaking, is ordinary calculus without limits
Perhaps due to the development of the fractional differential equations, an interest has been observed in studying boundary value problems of fractional q-difference equations, especially, about the existence of the solutions for the boundary value problems [5,6,7,8,9,10]
By means of fixed point theorems, sufficient conditions are obtained that guarantee the existence of solutions to the above boundary value problem
Summary
Roughly speaking, is ordinary calculus without limits. There are several types of quantum calculus: h-calculus ( known as the calculus of finite differences), qcalculus, and Hahn’s calculus. By means of fixed point theorems, sufficient conditions are obtained that guarantee the existence of solutions to the above boundary value problem.
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