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On a final value problem for fractional reaction‐diffusion equation with Riemann‐Liouville fractional derivative
Author(s) -
Tran Ngoc,
Au Vo Van,
Zhou Yong,
Huy Tuan Nguyen
Publication year - 2020
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.6103
Subject(s) - mathematics , fractional calculus , hadamard transform , uniqueness , bounded function , mathematical analysis , domain (mathematical analysis) , banach space , fixed point theorem
In this paper, we study a backward problem for a fractional diffusion equation with nonlinear source in a bounded domain. By applying the properties of Mittag‐Leffler functions and Banach fixed point theorem, we establish some results above the existence, uniqueness, and regularity of the mild solutions of the proposed problem in some suitable space. Moreover, we also show the ill‐posedness of our problem in the sense of Hadamard. The regularized solution is given, and the convergence rate between the regularized solution and the exact solution is also obtained.