A NOTE ON THE EXISTENCE OF SOLUTIONS FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

We study the existence of a unique bounded continuous solution of a Caputo fractional differential equation. The results are obtained from an equivalent Volterra integral equation which is derived by inverting the fractional differential equation. The kernel function of this integral equation is weakly singular, and hence the standard techniques that are normally used for Volterra integral equations do not apply here. This hurdle is overcome by using a resolvent equation, applying some known properties of the resolvent, and then employing the contraction mapping principle.