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arXiv · 2404.11486

On the non-local problem for Boussinesq type fractional equation

Ravshan Ashurov·Yusuf Fayziev·Muattar Khudoykulova
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Abstract

In recent years, the Boussinesq type fractional partial differential equation has attracted much attentions of researchers for its practical importance. In this paper we study a non-local problem for the Boussinesq type equation $D_t^αu(t)+A D_t^αu(t)+ν^2A u(t)=0,\,\, 0< t< T,\,\, 1<α<2,$ where $D_t^α$ is the Caputo fractional derivative and $A$ is abstract operator. In the classical case, i.e. at $α=2$, this problem was studied earlier and an interesting effect was discovered: the well-posedness of the problem significantly depends on the length of the time interval and the parameter $ν$. This note shows that for the case of a fractional equation there is no such effect: the problem is well-posed for any $T$ and $ν$.

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Ravshan Ashurov, Yusuf Fayziev, Muattar Khudoykulova. 2024-04-17. On the non-local problem for Boussinesq type fractional equation. https://arxiv.org/abs/2404.11486

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