In this manuscript, the existence, uniqueness, and stability of solutions to terminal value problem Riemann-Liouville fractional equations are established in variable exponent Lebesgue spaces L p ( . ) $$ {L}^{p(.)} We convert using generalized intervals piece-wise constant function. Further, Banach contraction principle is used, Ulam-Hyers-stability examined, finally, we construct an example.

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group Γ and relative Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum Λ ⊆ Γ , the norm of the Hilbert transform and th...