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Existence and regularity results of a backward problem for fractional diffusion equations
Author(s) -
Zhou Yong,
Wei He Jia,
Ahmad Bashir,
Huy Tuan Nguyen
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5781
Subject(s) - mathematics , uniqueness , bounded function , domain (mathematical analysis) , eigenvalues and eigenvectors , mathematical analysis , mittag leffler function , space (punctuation) , function (biology) , diffusion , fractional calculus , linguistics , philosophy , physics , quantum mechanics , evolutionary biology , biology , thermodynamics
In this paper, we study a backward problem for an inhomogeneous fractional diffusion equation in a bounded domain. By applying the properties of Mittag‐Leffler functions and the method of eigenvalue expansion, we establish some results about the existence, uniqueness, and regularity of the mild solutions as well as the classical solutions of the proposed problem in a weighted Hölder continuous function space.