Existence results for fractional hybrid differential systems in Banach algebras

In this manuscript we investigate the existence of solutions for the following system of fractional hybrid differential equations (FHDEs): $$ \textstyle\begin{cases} D^{p} [\frac{\theta(t)-w(t,\theta(t))}{u(t,\theta(t))}] = v(t,\vartheta (t)) ,\quad t \in J,\\ D^{p} [\frac{\vartheta(t)-w(t,\vartheta(t))}{u(t,\vartheta(t))}] = v(t,\theta(t)) ,\quad t \in J, 0 < p < 1,\\ \theta(0) = 0, \quad\quad \vartheta(0) = 0, \end{cases} $$ where \(D^{r}\) denotes the Riemann-Liouville fractional derivative of order r, \(J=[0,1]\), and the functions \(u:J\times \mathbb{R}\rightarrow\mathbb{R}\setminus\{0\}\), \(w:J\times \mathbb{R}\rightarrow\mathbb{R}\), \(w(0,0)=0\) and \(v:J\times\mathbb{R} \rightarrow\mathbb{R}\) satisfy certain conditions.