Inverse Cauchy problem for fractional telegraph equations with distributions
Journal Title: Карпатські математичні публікації - Year 2016, Vol 8, Issue 1
Abstract
The inverse Cauchy problem for the fractional telegraph equation $$u^{(\alpha)}_t-r(t)u^{(\beta)}_t+a^2(-\Delta)^{\gamma/2} u=F_0(x)g(t),\quad (x,t) \in {\rm R}^n\times (0,T],$$ 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.
Authors and Affiliations
H. P. Lopushanska, V. Rapita
Keywords
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- EP ID EP262978
- DOI 10.15330/cmp.8.1.118-126
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