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Existence and regularity results of a backward problem for fractional diffusion equations

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In this paper, we study a backward problem for an inhomogeneous fractional diffusion equation in a bounded domain. By applying the properties of Mittag‐Leffler functions and the method of eigenvalue… Click to show full abstract

In this paper, we study a backward problem for an inhomogeneous fractional diffusion equation in a bounded domain. By applying the properties of Mittag‐Leffler functions and the method of eigenvalue expansion, we establish some results about the existence, uniqueness, and regularity of the mild solutions as well as the classical solutions of the proposed problem in a weighted Hölder continuous function space.

Keywords: fractional diffusion; problem; existence regularity; backward problem

Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2019

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