Existence Results for a Coupled System of Nonlinear Fractional Hybrid Differential Equations with Homogeneous Boundary Conditions

Abstract

We study an existence result for the following coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions $D_{0^{+}}^{\alpha }[x(t)/f(t,x(t),y(t))]=g(t,x(t),y(t)),$ and $x(0)=y(0)=0,$ where $\alpha \in (\mathrm{0,1})$ and $D_{0^{+}}^{\alpha }$ denotes the Riemann-Liouville fractional derivative. The main tools in our study are the techniques associated to measures of noncompactness in the Banach algebras and a fixed point theorem of Darbo type.