On the non-local problem for Boussinesq type fractional equation

2024/04/17 by Ravshan Ashurov, Ashurov, Ravshan, Yusuf Fayziev +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2404.11486

openalex publication_date 2024/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)+ν²A 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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