Nontrivial solutions for fractional q-difference boundary value problems

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In this paper, we investigate the existence of nontrivial solutions to the nonlinear q-fractional boundary value problem

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Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences (2012, background): “1 [21] We note that if α > 0 and a ≤ b ≤ t , then (t − a) ≥ (t − b).”
Systems of semipositone discrete fractional boundary value problems (2014, background): “, [13,14,19,20,24,41]), linear systems of nabla fractional difference equations (e.”