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On a backward problem for fractional diffusion equation with Riemann‐Liouville derivative
Author(s) -
Tuan Nguyen Huy,
Tuan Nguyen Hoang,
Baleanu Dumitru,
Thach Tran Ngoc
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.5943
Subject(s) - mathematics , hadamard transform , fractional calculus , derivative (finance) , mathematical analysis , function (biology) , inverse problem , evolutionary biology , financial economics , economics , biology
In the present paper, we study the initial inverse problem (backward problem) for a two‐dimensional fractional differential equation with Riemann‐Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well‐posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L 2 and H τ norms is considered and illustrated by numerical example.