On the solutions of fractional hybrid differential equations

In this paper, we investigate the solutions of the following fractional order differential equation (FracDE) { cDt0α+[ x(t)−f1(t,x(t)) ]=f2(t,x(t),(It0β+x)(t)),∈J,x(t0)=x0∈ℝ where cDt0α+ is the Caputo fractional derivative of order 0 0. We prove the existence and uniqueness of the solution of above nonlinear FracDE under some conditions of f1 and f2. This result extends and complements some known results from the literature.