INVERSE COEFFICIENT PROBLEM FOR THE SEMI-LINEAR FRACTIONAL TELEGRAPH EQUATION

We establish the unique solvability for an inverse problem for semi-linear fractional telegraph equation D(t)(alpha)u r(t)D-l(beta) u - Delta u - Delta u = F0(x, t, u, D-l(beta) u), (x,t) is an element of Q(0) x (0, T] with regularized fractional derivatives D(t)(alpha)u, D-t(beta) u of orders alpha is an element of (1, 2), beta is an element of (0,1) with respect to time on bounded cylindrical domain. This problem consists in the determination of a pair of functions: a classical solution u of the first boundary-value problem for such equation, and an unknown continuous coefficient r(t) under the over-determination condition integral(Omega 0) u(x, t) phi (x)dx = F(t), t is an element of [0, T] with given functions phi and F.