The backward problem for time fractional evolution equations

2022/11/29 by S. E. Chorfi, Chorfi, S. E., L. Maniar +3 · 1 citation
Engineering · Mathematics · #26A33 #35R11 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2211.16493

openalex publication_date 2022/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the backward problem for fractional in time evolution equations ∂_t^αu(t)= A u(t) with the Caputo derivative of order 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.

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