New approach to existence of solution for weighted Cauchy-type problem

In this paper, we consider a singular differential equation involving Hilfer-Katugampola fractional derivative with the weighted initial condition. The Picard iterative technique has been successfully applied to obtain the existence of a unique solution. First, we derive an equivalent integral equation, then construct the successive approximations and use the ratio test to discuss its convergence. We demonstrate our results through a suitable illustrative example.

Keywords:

Fractional integrals and derivatives , Picard iterative technique , singular fractional differential equation , Cauchy-type problem