Inverse initial problem for a coupled system of fractional wave equations

We consider an inverse-initial problem for a coupled system of wave equations with theCaputo fractional derivatives. Using a method of separation of variables, we find a solution in a seriesform. Under certain conditions on the given data and fractional orders, we prove the unique solvability ofthe considered problem. Certain properties of Mittag-Leffler-type functions were crucial in evaluations.

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