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The stochastic heat inclusion with fractional time driven by time-space Brownian and L\'evy white noise
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt {\O}ksendal
https://arxiv.org/abs/2506.08275

The stochastic heat inclusion with fractional time driven by time-space Brownian and Lévy white noise
We study a time-fractional stochastic heat inclusion driven by additive time-space Brownian and Lévy white noise. The fractional time derivative is interpreted as the Caputo derivative of order $α\in (0,2).$ We show the following: \\ a) If a solution exists, then it is a fixed point of a specific set-valued map.\\ b) Conversely, any fixed point of this map is a solution of the heat inclusion.\\ c) Finally, we show that there is at least one fixed point of this map, thereby proving that there …