In the paper, we consider the problem of finding a solution to a fractional order equation of the form D^ₓu (t) +A (D^ₓu (t) ) +A^2 (D^ₓu (t) ) +Au (t) =f, 0<<1, and 0<t<T, satisfying the non-local condition u (T) =au (+0) +. Here a and T are given numbers, A: H H be a self-adjoint, unbounded, and positive operator defined on a separable Hilbert space H. In this work, we examine the role of the parameter a in determining the existence and uniqueness of solutions to the associated problem. Furthermore, we consider the inverse problem of reconstructing the right-hand side of the equation based on additional information about the solution.
Fayziev et al. (Sat,) studied this question.
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