New fixed point results in extended $b-$metric-like spaces via
simulation functions with applications
Abstract
The main ambition proposed in this article is to provide new fixed point
results for triangular $\alpha-$orbital admissible
contractions via some auxiliary and simulation functions in the frame of
extended $b-$metric-like spaces. As an application, we prove the
existence of a unique solution for a nonlinear fractional differential
equation with exponential weighted integral boundary conditions via the
generalized proportional fractional derivative of Caputo type with order
$\beta\in (n-1, n]$. Further, we
demonstrate the usability of our results through several examples.