Application of fixed point result to solve integral equation in the setting of graphical Branciari $ {\aleph } $-metric spaces

Abstract

In this present paper, we introduce graphical Branciari $ \aleph $-metric space and prove the fixed point theorem for $ \varOmega $-$ \mathcal{Q} $-contraction on complete graphical Branciari $ \aleph $ -metric spaces. Our result has been supplemented with suitable, non trivial examples. We have applied the derived fixed point result to solve non-linear Fredholm integral equations and fractional differential equation.

Keywords

• branciari $ \aleph $-metric space
• graphical branciari $ \aleph $-metric space
• $ \varomega $-$ \mathcal{q} $-contraction