On Fractional Duhamel's Principle

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.