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Abstract
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We explored a class of quantum calculus boundary value problems that include fractional
q-difference integrals. Sufficient and necessary conditions for demonstrating the existence and
uniqueness of positive solutions were stated using fixed point theorems in partially ordered spaces.
Moreover, the existence of a positive solution for a boundary value problem with a Riemann-Liouville
fractional derivative and an integral boundary condition was examined by utilizing a novel fixed point
theorem that included a a-η-Geraghty contraction. Several examples were provided to demonstrate the
efficacy of the outcomes.
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