(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
In this paper, we establish the existence and uniqueness of mild solutions for the time fractional hall-magneto-hydrodynamics stochastic equations with a fractional derivative of Caputo. Initially, we focus on the existence and uniqueness in the deterministe case. Using the Mittag-Leffler operators {Q_α(−t^α J): t ≥ 0} and {Q_α,α(−t^α J) : t ≥ 0} and applying the bilinear fixed-point theorem, we will prove the frist result. Next, by Itô integral, and by similair analogy we will establish the existence and uniqueness in the stochastic case in EN^μ_a ∩ N^2α_a,μ.