Analytical approach for time fractional wave equations in the sense of Yang-Abdel-Aty-Cattani via the homotopy perturbation transform method

Abstract

Very recently, Yang, Abdel-Aty and Cattani (2019) introduced a new and intersting fractional derivative operator with non-singular kernel involving Rabotnov fractional-exponential function. In this paper, we present a general framework of the homotopy perturbation transform method (HPTM) for analytic treatment of time fractional partial differential equations in the sense of Yang-Abdel-Aty-Cattani. As applications, time fractional wave equations involving Yang-Abdel-Aty-Cattani fractional derivatives are solved. The solutions are obtained in the form of series involving Prabhakar functions.