@article{Zili2024, 
author = {Mounir Zili and Eya Zougar and Mohamed Rhaima},
title = {Fractional stochastic heat equation with mixed operator and driven by fractional-type noise},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {28970-29000},
keywords = {stochastic fractional partial differential equations, fractional Brownian and sub-Brownian motions, mild solution, sample paths, heat equation},
url = {https://www.sciopen.com/article/10.3934/math.20241406},
doi = {10.3934/math.20241406},
abstract = {We investigated a novel stochastic fractional partial differential equation (FPDE) characterized by a mixed operator that integrated the standard Laplacian, the fractional Laplacian, and the gradient operator. The equation was driven by a random noise, which admitted a covariance measure structure with respect to the time variable and behaved as a Wiener process in space. Our analysis included establishing the existence of a solution in the general case and deriving an explicit form for its covariance function. Additionally, we delved into a specific case where the noise was modeled as a generalized fractional Brownian motion (gfBm) in time, with a particular emphasis on examining the regularity of the solution's sample paths.}
}