On the simultaneous reconstruction of the initial diffusion time and source term for the time-fractional diffusion equation

AbstractFacing application in real world, a simultaneous identification problem of determining the initial diffusion time (or the length of diffusion time) and source term in a time fractional diffusion equation is investigated. First the simultaneous reconstruction problem is proposed by translating the Caputo fractional derivative. Then the uniqueness results for the simultaneous identification problem are proven by the technique of analytic continuation and the Laplace transformation method. Next the Lipschitz continuousness of the observation operator is derived, and an alternating direction inversion algorithm is proposed to solve the simultaneous identification problem. At last, several numerical examples are computed to show the efficiency and stability of the reconstruction algorithm.Keywords: Simultaneous identificationthe length of diffusion timeinverse source problemuniquenesstime-fractional diffusion equation2000 MR Subject Classification: 65M0665M1265M32DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis work is supported by National Natural Science Foundation of China (12061008, 11861007, 11961002), Natural Science Foundation of Jiangxi Province of China (20202BABL 201004).