Explicit Analytical Solution for a kind of Time-Fractional Evolution Equations by He’s Homotopy Perturbation Methods

Abstract. In this letter, a kind of powerful analytical method, called Homotopy-perturbation method (HPM) is introduced to obtain the exact solutions for a kind of evolution equations with fractional derivatives. These initial value problems have signi?cant importance in applied science and many ?eld of engineering. In this method, a nonlinear complex differential equation is transformed to a series of linear and nonlinear parts, almost simpler di?erential equations. These sets of equations are then solved iteratively. ?nally, a linear series of the solutions completes the answer if the convergence is maintained. The results show that the proposed method is very e?cient and convenient and can readily be applied to a large class of fractional problems.