TY - JOUR AU - A. Ghanmi PY - 2019/01/25 Y2 - 2024/03/28 TI - Existence of positive solutions for a coupled system of nonlinear fractional differential equations JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 71 IS - 1 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1417 AB - We study the following nonlinear boundary-value problems for fractional differential equations$$D^{\alpha} u(t) = f(t, v(t),D^{\beta - 1}v(t)), t > 0,\\D^{\beta} v(t) = g(t, u(t),D^{\alpha - 1}u(t)), t > 0,\\u > 0,\; v > 0 \in (0,\infty),\lim_{t\rightarrow 0+}u(t) = \lim_{t\rightarrow 0+}v(t) = 0,$$where $1 < \alpha \leq 2$ and $1 < \beta \leq 2$. Under certain conditions on $f$ and $g$, the existence of positive solutions is obtained byapplying the Schauder fixed-point theorem. ER -