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Abstract

This article presents an analytical approximation for the nonlinearity of the fractional order gas dynamics equation in both homogeneous and nonhomogeneous cases, with a particular emphasis on shock fronts. The approach utilizes the fractional differentiation operator proposed by Atangana and Baleanu. By employing this operator, an approximate solution for the fractional order gas dynamic equations in scenarios involving shock fronts is derived. The solution process primarily involves an iterative procedure that leverages the Laplace transform for numerical computations. The use of the Laplace transform minimizes round-off errors, resulting in a solution that is both precise and straightforward to implement. The method's accuracy and reliability were validated using specific criteria of existence and uniqueness. Additionally, a table is included to demonstrate the method's effectiveness and capability, showing the absolute errors for particular values. Graphical illustrations are also provided to depict the solution's behavior and variations across different values. These visualizations aid in understanding the dynamics and complexities of the solutions obtained using the Atangana-Baleanu operator. Overall, the method proves to be a robust and efficient tool for solving fractional order gas dynamic equations, offering significant precision and ease of application.

Keywords

Atangana-Baleanu Operator, Fractional Differential Equations, Fractional Gas Dynamic Equations, Iterative Laplace Transform Method, Numerical Solutions

Subject Area

Mathematics

Article Type

Article

First Page

2386

Last Page

2401

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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