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| Abdellatif Ghendir Aoun |
| Abdellatif Ghendir Aoun |
| (Ecole Normale Supérieure, 16050 Kouba, Algiers, Algeria) |
| DOI： |
| Abstract: |
| In this paper, we study a fractional differential equation $$^{c}D^{\alpha}_{0^{+}}u(t)+f(t,u(t))=0,\quad t\in(0, +\infty)$$ satisfying the boundary conditions:
$$u^{\prime}(0)=0,\quad \lim_{t\rightarrow +\infty}\,^{c}D^{\alpha-1}_{0^{+}}u(t)=g(u),$$ where $1<\alpha\leqslant2$, $^{c}D^{\alpha}_{0^{+}}$ is the standard Caputo fractional derivative of order $\alpha$. The main tools used in the paper is contraction principle in the Banach space and the fixed point theorem due to
D. O'Regan. Some the compactness criterion and existence of solutions are established. |
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