A new fixed point approach for solutions of a $p$-Laplacian fractional $q$-difference boundary value problem with an integral boundary condition

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 $\mathfrak{a}$- $\eta$-Geraghty contraction. Several examples were provided to demonstrate the efficacy of the outcomes.