Asymptotically Weyl almost periodic functions in Lebesgue spaces with variable exponents

In this paper, we introduce and analyze several different notions of Weyl almost periodic functions ergodic components in Lebesgue spaces with variable exponent Lp(x). We investigate the invariance (asymptotical) periodicity under actions convolution products, providing also some illustrative applications to abstract fractional differential inclusions Banach spaces. The introduced classes generalized (asymptotically) are new even case that function p(x) has a constant value p≥1, provided ϕ(x) F(l,t) our consideration satisfy ϕ(x)≠x or F(l,t)≠l(−1)/p.