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For ∈ (0, 1), we investigate the nonlinear integro-differential equation on a multidi-where is the Caputo fractional derivative and  1 and  2 are uniform elliptic operators with smooth coefficients depending on time. Under suitable conditions on the nonlinearity, the global existence and uniqueness of the classical solution to the related initial and boundary value problems are established. K E Y W O R D S a priori estimates, Caputo derivative, materials with memory, subdiffusion M S C ( 2 0 1 0 ) 35C15, 35R11, 45N05 1490

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We analyze the inverse boundary value-problem to determine the fractional order ν of nonautonomous semilinear subdiffusion equations with memory terms from observations of their solutions during small time. We obtain an explicit formula reconstructing the order. Based on the Tikhonov regularization scheme and the quasi-optimality criterion, we construct the computational algorithm to find the order ν from noisy discrete measurements. We present several numerical tests illustrating the algorithm in action.

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