Existence of solutions for fractional differential equations with Dirichlet boundary conditions
Year: 2016
Type: article
Abstract: In this article, we apply the Nehari manifold to prove the existence of a solution of the fractional differential equation $$\displaylines{ \frac{d}{dt} \Big(\frac12 {\,}_0D_t^{-\beta}(u'(t)) +\frac12 {\,}_tD_T^{-\beta}(u'(t)))= f(t,u(t)) + \lambda h(t)|u(t)|^{r-2}u(t), \cr \text{a.e } t\in [0,T],\cr u(0)=u(T)=0, }$$ where $ _0D_t^{-\beta},\; _tD_T^{-\beta}$ are the left and right Riemann-Liouville fractional integrals, respectively, of order $0< \beta < 1$.
Authors: Khaled Ben Ali, Abdeljabbar Ghanmi, Khaled Kefi
Institutions: Tunis University, University of Jeddah
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387637192