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A new coupling method of khalouta transform and residua lpower series method for solving nonlinear fractional hyperbolic-like equations with variable coefficients

Khalouta Ali

Journal of Applied Mathematics and Computational Mechanics

2025

Vol. 24, nr 1

30--43

In this paper, we develop a new numerical method called Khalouta residual power series method (KHRPSM) by mixing the Khalouta transform method and the residual power series method for solving nonlinear fractional hyperbolic-like equations with variable coefficients. The KHRPSM resolves nonlinear fractional problems without resorting to He’s polynomials and Adomian polynomials. Therefore, the small computational size of this method is the strength of the scheme, which is an advantage compared with various series solution methods. The approximate and exact solutions of a numerical example of the proposed problem are demonstrated by the presented method. The numerical and exact solutions are compared with each other. The obtained results show that KHRPSM is easy to implement and highly effective in constructing approximate analytical solutions to nonlinear fractional problems arising in related fields of science and technology.