Abstract
In this paper, we discuss the existence of weak solutions for a nonlinear boundary value problem of fractional q-difference equations in Banach space. Our analysis relies on the Monch’s fixed-point theorem combined with the technique of measures of weak noncompactness.
Highlights
Fractional differential calculus is a discipline to which many researchers are dedicating their time, perhaps because of its demonstrated applications in various fields of science and engineering [ ]
Many researchers studied the existence of solutions to fractional boundary value problems, for example, [ – ]
The q-difference calculus or quantum calculus is an old subject that was initially developed by Jackson [, ]; basic definitions and properties of q-difference calculus can be found in [, ]
Summary
Fractional differential calculus is a discipline to which many researchers are dedicating their time, perhaps because of its demonstrated applications in various fields of science and engineering [ ]. Many researchers studied the existence of solutions to fractional boundary value problems, for example, [ – ]. Maybe due to the explosion in research within the fractional differential calculus setting, new developments in this theory of fractional q-difference calculus were made, for example, q-analogues of the integral and differential fractional operators properties such as Mittage-Leffler function [ ], just to mention some. El-Shahed and Hassan [ ] studied the existence of positive solutions of the q-difference boundary value problem:. Ferreira [ ] considered the existence of positive solutions to nonlinear q-difference boundary value problem:. < t < , < α ≤ , Ferreira [ ] studied the existence of positive solutions to nonlinear q-difference boundary value problem:. El-Shahed and Al-Askar [ ] studied the existence of positive solutions to nonlinear q-difference equation:
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