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

Abstract

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.

Keywords

• fractional derivatives
• quantom calculus
• differential equations
• boundary value problems
• positive solution