Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann–Liouville fractional integrals, and Atangana–Baleanu integral operators

Abstract In this manuscript, some fixed point results for generalized contractive type mappings under mild conditions in the setting of double controlled metric spaces (in short, $\eta _{\gimel }^{\nu }$ η ℷ ν -metric spaces) are obtained. Moreover, related consequences dealing with a common concept and nontrivial examples to support our presented. Ultimately, we use theoretical discuss existence uniqueness solutions 2D Volterra integral equations, Riemann–Liouville integrals Atangana–Baleanu operators given.