This research explores solutions to a fractional order equation in a separable Hilbert space, indicating the importance of parameters in solution uniqueness.
In the paper, we consider the problem of finding a solution to a fractional order equation of the form Dαₜu(t)+A(Dαₜu(t))+A²(Dαₜu(t))+Au(t)=f , 0<α<1 , and $$0<t<T$$ , satisfying the non-local condition u(T)=au(+0)+φ . 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.
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Fayziev et al. (2025) studied this question.
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