Li, Zhiyuan; Cheng, Xing; Li, Gongsheng An inverse problem in time-fractional diffusion equations with nonlinear boundary condition. (English) Zbl 1480.60240 J. Math. Phys. 60, No. 9, 091502, 18 p. (2019). Summary: This paper deals with the 1D time-fractional diffusion equations with nonlinear boundary condition. We first give an integral equation of the solution via the theta-function and eigenfunction expansion and establish the short time asymptotic behavior of the solution. We then verify the uniqueness of the inverse problem in determining the fractional order by the one endpoint observation whether the nonlinear boundary condition is known or not. Furthermore, in the case when the nonlinear boundary condition is known, we can establish the Lipschitz stability of the fractional order with respect to the measured data at the one endpoint by using the Lipschitz continuity of the solution with respect to the fractional order.©2019 American Institute of Physics Cited in 5 Documents MSC: 60J60 Diffusion processes 60G22 Fractional processes, including fractional Brownian motion 14K25 Theta functions and abelian varieties 45C05 Eigenvalue problems for integral equations 45M05 Asymptotics of solutions to integral equations 45Q05 Inverse problems for integral equations 26A16 Lipschitz (Hölder) classes PDFBibTeX XMLCite \textit{Z. Li} et al., J. Math. Phys. 60, No. 9, 091502, 18 p. (2019; Zbl 1480.60240) Full Text: DOI References: [1] Benson, D. A.; Wheatcraft, S. W.; Meerschaert, M. M., Application of a fractional advection-dispersion equation, Water Resour. 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