A Semi-Analytical Method to Investigate Fractional-Order Gas Dynamics Equations by Shehu Transform

Abstract

This work aims at a new semi-analytical method called the variational iteration transformation method for solving nonlinear homogeneous and nonhomogeneous fractional-order gas dynamics equations. The Shehu transformation and the iterative technique are applied to solve the suggested problems. The proposed method has an advantage over existing approaches because it does not require additional materials or computations. Four problems are used to test the authenticity of the proposed method. Using the suggested method, the solution proves to be more accurate. The proposed method can be implemented to solve many nonlinear fractional order problems because it has a straightforward implementation.

Keywords

• variational iteration method
• Shehu transform
• gas dynamics equation
• Mittag–Leffler function
• Caputo derivatives