  In this work, we establish some abstract results on the perspective of the
fractional Musielak-Sobolev spaces, such as: uniform convexity, Radon-Riesz
property with respect to the modular function, $(S_{+})$-property, Brezis-Lieb
type Lemma to the modular function and monotonicity results. Moreover, we apply
the theory developed to study the existence of solutions to the following class
of nonlocal problems
  \begin{equation*}
  \left\{
  \begin{array}{ll}
  (-\Delta)_{\Phi_{x,y}}^s u = f(x,u),& \mbox{in }\Omega,
  u=0,& \mbox{on }\mathbb{R}^N\setminus \Omega,
  \end{array}
  \right.
  \end{equation*}
  where $N\geq 2$, $\Omega\subset \mathbb{R}^N$ is a bounded domain with
Lipschitz boundary $\partial \Omega$ and $f:\Omega \times \mathbb{R}
\rightarrow \mathbb{R}$ is a Carath\'{e}odory function not necessarily
satisfying the Ambrosetti-Rabinowitz condition. Such class of problems enables
the presence of many particular operators, for instance, the fractional
operator with variable exponent, double-phase and double-phase with variable
exponent operators, anisotropic fractional $p$-Laplacian, among others.
