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 proportional to of a function f(t)
I-t (proportional to)(s)(AB)zeta(t) = 1 - proportional to/B(proportional to) zeta(t) + alpha/B(proportional to)Gamma(proportional to)integral(t)(0) zeta(rho)(t - rho)(proportional to-1) d rho;
where 0 < proportional to <= 1,0 < t < s and it is worthy to mention B(0) and B(1) are equal to 1.
(b): L-P type solution (1 < p < infinity) for the linear Fredholm integral equation of the second kind
alpha(t) = psi(t) + proportional to integral(infinity)(0) -g(p, t)alpha(rho)d rho;
where
alpha,psi is an element of L-P(0, infinity)
(C) 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).