Comparison of third-order fractional partial differential equation based on the fractional operators using the explicit finite difference method

Abstract

In this research paper, the third-order fractional partial differential equation (FPDE) in the sense of the Caputo fractional derivative and the Atangana-Baleanu Caputo (ABC) fractional derivative is investigated for the first time. The importance of the proposed problem is more general than the third-order linear time-varying systems model. This fractional partial differential equation is converted to the abstract form of the ordinary differential equation at β = 1. A first-order finite difference scheme is created for the converted problem. The stability inequality of the (FDS) is demonstrated for this abstract form problem using Cardano's relation method in Hilbert space. The explicit finite difference method (EFDM) is used to obtain an approximate solution of the third-order fractional partial differential equation (FPDE) based on the Caputo fractional derivative and the (ABC) fractional derivative of order β∈(0,1]. Concerning these equations, the obtained approximate solutions using the proposed method are contrasted with the exact solution. Finally, the simulation for the third-order (FPDE) based on the fractional derivatives of Caputo and (ABC) for both the exact and approximate solutions is given.

Keywords

• Fractional partial differential equation
• Caputo fractional derivative
• ABC fractional derivative
• Finite difference method
• Stability estimates
• Approximate solution