Identification of the Memory Order in Multi-Term Semilinear Subdiffusion

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In this paper, we analyze the inverse problem of determining the order ν of the major derivative in the multi-term fractional in time semilinear diffusion equation with memory terms. This framework is relevant to the oxygen transport through capillaries. We obtain an explicit formula reconstructing the order ν for small time state measurements. Appealing to the Tikhonov regularization scheme and the quasi-optimality criterion, we propose the computational algorithm to recovery ν from noisy discrete measurements. We provide several numerical tests illustrating the effectiveness of this algorithm in practice.