Bayesian approach for identifying fractional order and time-dependent source in a fractional pseudo-parabolic equation

In this paper, the inverse problem of identifying fractional order and time-dependent source term for fractional pseudo-parabolic equation is investigated. We prove that the simultaneous recovery of the fractional order and the source term is unique, and then give the estimate of measurement data. Such problem is formulated into Bayesian inverse problem, and the continuity of forward mapping is proved. Moreover, the iterative regularizing ensemble Kalman method is applied to solve Bayesian inverse problem and two numerical examples are conducted to show its efficiency.