Abstract:A nonlocal boundary value problem for the fractional version of the Rayleigh–Stokes equation, well-known in fluid dynamics, is studied. Namely, the condition u(x,T)=βu(x,0)+φ(x), where β is an arbitrary real number, is proposed instead of the initial condition. If β=0, then we have the inverse problem in time, called the backward problem. It is well-known that the backward problem is ill-posed in the sense of Hadamard. If β=1, then the corresponding non-local problem becomes well-posed in the sense of Hadamard… Show more
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