# Inverse Cauchy problem for fractional telegraph equations with distributions

## Keywords:

generalized function, fractional derivative, inverse problem, Green vector-function
Published online:
2016-06-30

### 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.

How to Cite

(1)

Lopushanska, H.; Rapita, V. Inverse Cauchy Problem for Fractional Telegraph Equations With Distributions.

*Carpathian Math. Publ.***2016**,*8*, 118-126.