J. Nonl. Mod. Anal., 7 (2025), pp. 1369-1382.
Published online: 2025-07
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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 $\mathcal{EN}^{\mu}_a ∩ N^{2α}_{a,\mu}.$
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1369}, url = {http://global-sci.org/intro/article_detail/jnma/24241.html} }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 $\mathcal{EN}^{\mu}_a ∩ N^{2α}_{a,\mu}.$