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The backward problem for time-fractional evolution equations.

Authors :
Chorfi, S. E.
Maniar, L.
Yamamoto, M.
Source :
Applicable Analysis; Aug2024, Vol. 103 Issue 12, p2194-2212, 19p
Publication Year :
2024

Abstract

In this paper, we consider the backward problem for fractional in time evolution equations $ \partial _t^\alpha u(t)= A u(t) $ ∂ t α u (t) = Au (t) with the Caputo derivative of order $ 0 0 < α ≤ 1 , where A is a self-adjoint and bounded above operator on a Hilbert space H. First, we extend the logarithmic convexity technique to the fractional framework by analyzing the properties of the Mittag–Leffler functions. Then we prove conditional stability estimates of Hölder type for initial conditions under a weaker norm of the final data. Finally, we give several applications to show the applicability of our abstract results. [ABSTRACT FROM AUTHOR]

Subjects

Subjects :
HILBERT space

Details

Language :
English
ISSN :
00036811
Volume :
103
Issue :
12
Database :
Complementary Index
Journal :
Applicable Analysis
Publication Type :
Academic Journal
Accession number :
179022830
Full Text :
https://doi.org/10.1080/00036811.2023.2290273