Novel fixed point approach to Atangana-Baleanu fractional and L p -Fredholm integral equations

Abstract

In this article, we introduce an extended F-metric and proved related fixed point results. Subsequently, we mainly focus on (a): Solution for the Atangana-Baleanu fractional integral of order ∝ of a function f(t) It∝sABζ(t)=1-∝B(∝)ζ(t)+∝B(∝)Γ(∝)∫0tζ(ρ)(t-ρ)∝-1dρ; where 0<∝⩽1,0<t<s and it is worthy to mention B(0) and B(1) are equal to 1. (b): LP type solution (1<p<∞) for the linear Fredholm integral equation of the second kind where