AbstractThis paper is devoted to the study of the existence of solution to the following system of fractional hybrid differential equations: $$ \textstyle\begin{cases} D^{p} [x(t)- f(t,x(t))] = g (t,y(t),I^{\alpha}(y(t))) ,\quad \mbox{a.e. }t \in J, \\ D^{p} [y(t)- f(t,y(t))] = g (t,x(t),I^{\alpha}(x(t))) ,\quad \mbox{a.e. }t \in J, 0 < p < 1, \alpha>0, \\ x (0) = 0,\qquad y (0) = 0, \end{cases} $$ { D p [ x ( t ) − f ( t , x ( t ) ) ] = g ( t , y ( t ) , I α ( y ( t ) ) ) , a.e. t ∈ J , D p [ y ( t ) − f ( t , y ( t ) ) ] = g ( t , x ( t ) , I α ( x ( t ) ) ) , a.e. t ∈ J , 0 < p < 1 , α > 0 , x ( 0 ) = 0 , y ( 0 ) = 0 , where $D^{\alpha}$ D α is the R-L fractional derivative of order α, $J=[0,T]$ J = [ 0 , T ] , $T>0$ T > 0 , and the functions $f :J\times\mathbb{R} \times\mathbb{R} \rightarrow\mathbb{R}$ f : J × R × R → R , $f(0,0)=0$ f ( 0 , 0 ) = 0 and $g:J \times\mathbb{R} \times\mathbb{R}\rightarrow\mathbb{R}$ g : J × R × R → R satisfy certain conditions.The proof of the existence theorem is based on a coupled fixed point theorem of Krasnoselskii type, which extends a fixed point theorem of Burton (Appl. Math. Lett. 11:85-88, 1998). Finally, our results are illustrated by a concrete example.