The backward problem for time fractional evolution equations

S. E. Chorfi; L. Maniar; M. Yamamoto

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arXiv · 2211.16493

The backward problem for time fractional evolution equations

S. E. Chorfi·L. Maniar·M. Yamamoto

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Abstract

In this paper, we consider the backward problem for fractional in time evolution equations $\partial_t^\alpha u(t)= A u(t)$ with the Caputo derivative of order $0<\alpha \le 1$, 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 H\"older 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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S. E. Chorfi, L. Maniar, M. Yamamoto. 2022-11-29. The backward problem for time fractional evolution equations. https://arxiv.org/abs/2211.16493

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