2021-02-012021-02-012020-06-11NGuyen, H.T. y Caraballo Garrido, T. (2020). ON INITIAL AND TERMINAL VALUE PROBLEMS FOR FRACTIONAL NONCLASSICAL DIFFUSION EQUATIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 149 (1), 143-1-161-19.1088-6826https://hdl.handle.net/11441/104392In this paper, we consider fractional nonclassical diffusion equations under two forms: initial value problem and terminal value problem. For an initial value problem, we study local existence, uniqueness, and continuous dependence of the mild solution. We also present a result on unique continuation and a blow-up alternative for mild solutions of fractional pseudo-parabolic equations. For the terminal value problem, we show the well-posedness of our problem in the case 0 < α ≤ 1 and show the ill-posedness in the sense of Hadamard in the case α > 1. Then, under the a priori assumption on the exact solution belonging to a Gevrey space, we propose the Fourier truncation method for stabilizing the ill-posed problem. A stability estimate of logarithmic-type in Lq norm is first established.application/pdf19 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Fractional nonclassical diffusion equationwell-posednessill-posednessregularity estimatesregularization and error estimateinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1090/proc/15131