Initial time difference quasilinearization method for fractional differential equations involving generalized Hilfer fractional derivative

Abstract

We build the quasilinearization method with initial time difference for nonlinear fractional differential equations (FDEs) involving generalized Hilfer fractional derivative under various conditions on the nonlinear function involved in the right hand side of the equation. An essential comparison result concerning lower and upper solutions is obtained for this generalized FDEs without demanding the Holder continuity assumption.