Abstract
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 \(\mathcal{E}\mathcal{N}_{p}^{\lambda } \cap \textrm{N}_{p,\lambda }^{2\alpha }\).
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Khaider, H., Azanzal, A., Abderrahmane, R. et al. Mild solution for the time fractional magneto-hydrodynamics system. Anal.Math.Phys. 14, 14 (2024). https://doi.org/10.1007/s13324-024-00871-9
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DOI: https://doi.org/10.1007/s13324-024-00871-9