On parabolic problems with fractional q(z)-Laplacian operators and young measures

In this paper, we establish the existence of weak solutions for a parabolic problem involving the fractional q(z)-Laplacian operator \((-\Delta )_{q(z)}^\sigma \) ${(-\mathrm{\Delta })}_{q(z)}^{\sigma }$ . The main results are derived using the Young measures method combined with generalized Lebesgue and Sobolev spaces with variable exponents, alongside the Galerkin approximation. Our results expand upon and broaden several recent studies in this area of literature