In the present work, a hybrid of Fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. The Fourier transform is employed with combination of homotopy perturbation method (HPM), the so called Fourier transform homotopy perturbation method (FTHPM) to solve the partial differential equations. The c...

n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

sufficient conditions are established under which the zero solution x = 0 of equation (2) isunstable.

Abstract Two types of second-order in time partial differential equations, namely semilinear wave equations and beam are considered. To solve these with exponential integrators, we present an approach to compute efficiently the action matrix as well those related functions. Various numerical simulations presented that illustrate this approach.