  We consider the nonlinear Cauchy problem for $ \Psi $- Hilfer fractional
differential equations and investigate the existence, interval of existence and
uniqueness of solution in the weighted space of functions. The continuous
dependence of solutions on initial conditions is proved via Weissinger fixed
point theorem. Picard's successive approximation method has been developed to
solve nonlinear Cauchy problem for differential equations with $ \Psi $- Hilfer
fractional derivative and an estimation have been obtained for the error bound.
Further, by Picard's successive approximation, we derive the representation
formula for the solution of linear Cauchy problem for $ \Psi $-Hilfer
fractional differential equation with constant coefficient and variable
coefficient in terms of Mittag-Leffler function and Generalized (Kilbas-Saigo)
Mittag-Leffler function.
