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Fractional Landweber method for an initial inverse problem for time-fractional wave equations. (English) Zbl 1460.35375

Summary: In this paper, we consider the initial inverse problem (backward problem) for an inhomogeneous time-fractional wave equation in a general bounded domain. We show that the backward problem is ill-posed, and we propose a regularizing scheme using a fractional Landweber regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.

MSC:

35R11 Fractional partial differential equations
35A25 Other special methods applied to PDEs
35R30 Inverse problems for PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
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