Space-time fractional SPDEs with locally Lipschitz coefficients: well-posedness

Ngartelbaye Guerngar, Erkan Nane

In this article, we study the space-time SPDE $${\partial }_t^{2}u=-(-\hat{I}”{)}^{\hat{I}\pm /2}u+I_t^{1-{\hat{I}}^2}[b(u)+\ddot{I}ƒ(u)\dot{W}],$$ where $u=u(t,x)$ is defined for $(t,x)\in\mathbb{R}_+\times \mathbb…