Abstract

Abstract

In this paper, a new fractional analytical iterative method was successfully used to obtain the fractional analytical solutions of the homogeneous nonlinear gas dynamics equation and nonlinear convection-diffusion equation. The novelty of the paper appears in its specific application of the Caputo fractional operator to conventional equations while achieving extremely precise solutions through familiar series solutions and for more complex nonlinear solutions to fractional partial differential equations. Also, no assumptions about nonlinear terms are needed. Numerical outcomes for various cases of the equations are represented via tables and graphs. The convergence analysis for the present approach was successfully completed. The methodology is very capable of reducing the size of the analytical steps as well as being convenient and efficient for solving nonlinear fractional equations.

Abstract

In this paper, a new analytical iterative method is used to obtain the fractional analytical solutions of the nonlinear gas dynamics and convectiondiffusion equations. The paper’s novelty appears in its specific application of the Caputo fractional operator to conventional equations while achieving highly accurate solutions. Numerical outcomes for various cases of the equations are represented via tables and graphs. The convergence analysis for the present approach was completed. The methodology is very capable of reducing the size of the analytical steps and is convenient and efficient for solving nonlinear fractional equations. The Temimi-Ansari method’s applicability across different types of fractional differential equations indicates its potential as a powerful tool in solving nonlinear fractional models in diverse scientific and technical fields.OPEN ACCESS Received: 19/07/2024 Accepted: 11/11/2024 Published: 07/04/2025