Initial time difference quasilinearization for Caputo Fractional Differential Equations

This paper deals with an application of the method of quasilinearization by not demanding the Holder continuity assumption of functions involved and by choosing upper and lower solutions with initial time difference for nonlinear Caputo fractional differential equations. Thus, we construct monotone flows that are generated by solutions of linear fractional differential equations which converge uniformly and quadratically to the unique solution of the problem. Also, necessary comparison result concerning lower and upper solutions are proved without using Holder continuity.