In this paper, by using the Mittag–Leffler operators \(\{\mathcal {L}_{\alpha }(-t^{\alpha }\mathbb {I}):t\ge 0\}\) and \(\{\mathcal {L}_{\alpha ,\alpha }(-t^{\alpha }\mathbb {I}):t\ge 0\}\) we will prove the mild soltion of the time fractional magneto-hydrodynamics system with a fractional derivative of Caputo. Furthermore, by Itô integral, we will establish the mild solution of stochastic time fractional magneto-hydrodynamics system in \(\mathcal{E}\mathcal{N}_{p}^{\lambda } \cap \textrm{N}_{p,\lambda }^{2\alpha }\).

中文翻译：

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时间分数磁流体动力学系统的温和解

在本文中，通过使用 Mittag–Leffler 算子\(\{\mathcal {L}_{\alpha }(-t^{\alpha }\mathbb {I}):t\ge 0\}\)和\ (\{\mathcal {L}_{\alpha ,\alpha }(-t^{\alpha }\mathbb {I}):t\ge 0\}\)我们将证明时间分数磁电机的温和解-具有卡普托分数阶导数的流体动力学系统。此外，通过 Itô 积分，我们将在\(\mathcal{E}\mathcal{N}_{p}^{\lambda } \cap \textrm{N}_中建立随机时间分数磁流体动力学系统的温和解{p,\lambda}^{2\alpha}\)。