Inverse Cauchy problem for fractional telegraph equations with distributions - Lopushanska, H.P.; Rapita, V. (Carpathian Mathematical Publications, 2016)
The inverse Cauchy problem for the fractional telegraph equation u^(α)_t-r(t)u^(β)_t+a^2(-Δ)^γ/2 u=F_0(x)g(t), (x,t) R^n× (0,T], with given distributions in the right-hand sides of the equation and initial conditions is studied. Our task is to determinate a pair of functions: a generalized solution u (continuous in time variable in general sense) and unknown continuous minor coefficient r(t). The unique solvability of the problem is established.