A Study on k-Generalized -Hilfer Derivative Operator

In this paper, we generalize the psi-Hilfer fractional derivative and discuss some of its properties. We prove existence, uniqueness and stability results for a class of initial value problems for implicit nonlinear fractional differential equations involving generalized psi-Hilfer fractional derivative. The uniqueness result for the given problem is obtained via the Banach contraction mapping principle. In addition, two examples are given to illustrate our results.