TY - JOUR
T1 - Mild Solution for the Time Fractional Hall-Magneto-Hydrodynamics Stochastic Equations
AU - Khaider , Hassan
AU - Azanzal , Achraf
AU - Raji , Abderrahmane
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1369
EP - 1382
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1369
UR - https://global-sci.org/intro/article_detail/jnma/24241.html
KW - Time fractional hall-magneto-hydrodynamics equations, Itô integral, derivative of Caputo, stochastic.
AB - <p style="text-align: justify;">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 $\{\mathcal{Q}_α(−t^α \mathbb{J}): t ≥ 0\}$ and $\{\mathcal{Q}_{α,α}(−t^α \mathbb{J}) : t ≥ 0\}$ 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 $\mathcal{EN}^{\mu}_a ∩ N^{2α}_{a,\mu}.$</p>