Mild solution for the time fractional magneto-hydrodynamics system. (English) Zbl 1535.35145
Summary: In this paper, by using the Mittag-Leffler operators \(\{\mathcal{L}_\alpha(-t^\alpha\mathbb{I}): t \geq 0\}\) and \(\{\mathcal{L}_{\alpha,\alpha}(-t^\alpha\mathbb{I}): t \geq 0\}\) 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 \(\mathcal{EN}_p^\lambda \cap \mathrm{N}_{p, \lambda}^{2\alpha}\).
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 60H05 | Stochastic integrals |
| 35R11 | Fractional partial differential equations |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
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