Abstract:
In this academic research we generalized the Duhamel's principle and extended this
principle for the higher order integer and fractional psi di erential equation subject to
suitable initial conditions. Furthermore, as application of the generalized Duhamel's
principle, some notions like stability, existence and uniqueness of the solutions of the
generalized fractional di erential equation with initial conditions is investigated. In
order to approximate the solutions of the generalized nonlinear fractional di erential
equation with initial conditions, we introduce a new numerical technique combining
the Haar wavelets and Duhamel's principle called Haar-Duhamel's method.
