We establish the well-posedness of the Cauchy problem and the two-point boundary-value problem for an equation with an operator of fractional differentiation that corresponds to the singular parabolic Beltrami – Laplace operator on a surface of the Dini class.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 8, pp. 1088–1097, August, 2009.
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Matiichuk, M.I. Problems for equations with special parabolic operator of fractional differentiation. Ukr Math J 61, 1289–1301 (2009). https://doi.org/10.1007/s11253-010-0276-z
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DOI: https://doi.org/10.1007/s11253-010-0276-z