An inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion
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We study the inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion with Hurst index H∈(0,1). With the aid of a novel estimate, by using the operator approach we propose regularity analyses for the direct problem. Then we provide a reconstruction scheme for the source terms f and g up to the sign. Next, combining the properties of Mittag-Leffler function, the complete uniqueness and instability analyses are provided. It's worth mentioning that all the analyses are unified for H∈(0,1).
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