Mathematics & Physics 2015, 8(1), 55–63 УДК 517.986.7 Parameter Determination in a Differential Equation of Fractional Order with Riemann-Liouville Fractional Derivative in a Hilbert Space Dmitry G.Orlovsky∗ National Research Nuclear University MEPhI Kashirskoye shosse, 31, Moscow, 115409 Russia Received 10.10.2014, received in revised form 20.11.2014, accepted 15.12.2014 The Cauchy type problem for a differential equation with fractional derivative and self-adjoint operator in a Hilbert space is considered. <...> The problem of parameter determination in equation by the value of the solution at a fixed point is presented. <...> Keywords: equation of fractional order, Hilbert space, self-adjoint operator, Cauchy-type problem, MittagLeffler function, inverse problem, characteristic function. <...> Introduction In recent years, theory of differential equations with fractional derivatives has attracted considerable interest. <...> One of the modern methods for studying equations of mathematical physics is the theory of differential equations in Banach and Hilbert spaces. <...> Abstract differential equations of fractional order are considered in [5–8]. <...> All rights reserved c – 55 – t 0 t 0 (t−s)α ds, u(s) u(s) (t−s)α ds (1) (2) Dmitry G.Orlovsky Parameter Determination in a Differential Equation of Fractional Order . and Γ is the Gamma function. <...> A solution of (1), (2) is a continuous function u(t) in H for t > 0 such that Dα−1u(t) is continuously differentiable in H for t > 0. <...> If space H has the Radon-Nikodym property (every absolutely continuous function represented by the integral of its derivative) then problem (3), (4) is uniformly well-posed if and only if when Reλ > ω the operator A has the resolvent R(λα) = (λαI −A)−1. <...> In this case the solution operator has the following representation [9] V (t) = D1−α 1 ω0−i∞ Let us consider the Cauchy type problem (1), (2) assuming that problem is uniformly wellposed. <...> The solvability of this problem can be proved if (C1) functions f(t) and Af(t) are continuous for t > 0 in H and absolutely integrable at t = 0; (C2) function Dα−1f(t) is continuous <...>