### Inverse Cauchy problem for fractional telegraph equations with distributions

#### Abstract

The inverse Cauchy problem for the fractional telegraph equation

$$u^{(\alpha)}_t-r(t)u^{(\beta)}_t+a^2(-\Delta)^{\gamma/2} u=F_0(x)g(t), \;\;\; (x,t) \in {\rm R}^n\times

(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.

#### Keywords

generalized function, fractional derivative, inverse problem, Green vector-function

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