A SPECTRAL COLLOCATION SCHEME WITH 2D ULTRASPHERICAL WAVELETS FOR FRACTIONAL NONLINEAR GAS DYNAMICS EQUATIONS UNDER CAPUTO–FABRIZIO DERIVATIVE

Gas Dynamics Equations (GDEs) play a fundamental role in modeling fluid flows phenomena across a range of applications, from environmental systems to aerospace engineering. These equations mathematically represent the fundamental laws of mass, momentum and energy conservation. Modeling complex gas flows often requires advanced mathematical tools capable of capturing nonlocal and memory-dependent behavior. Therefore, this study explores the implementation of the Caputo–Fabrizio Fractional Derivative (CFFD) in the analysis of GDEs, highlighting its potential to accurately capture the behavior of complex fluid dynamics systems. A two-dimensional (2D) wavelet-based approach combined with suitable collocation grids is employed to approximate the solutions for spacetime Fractional Gas Dynamics Equations (FGDEs). The concept of the CFFD, with its nonsingular kernel, is integrated into the framework of GDEs, offering a more precise analytical perspective. By reformulating the FGDEs into a system of algebraic equations, the proposed approach enables efficient computation via iterative technique. The error analysis of the numerical results is presented through graphs and tables for three illustrative examples with varying fractional values, demonstrating a strong correlation between the analytical and approximated solutions. The performance of the scheme is evaluated using multiple error metrics, including minimum absolute error, [Formula: see text] error, [Formula: see text] error, and [Formula: see text] errors. The absolute errors demonstrate the improvement in results of FGDEs as the wavelet basis increases. The results validate the reliability and ease of implementation of the suggested approach for solving the FGDEs. The study demonstrates the method’s reliability, and potential for solving a wide class of nonlinear fractional models governed by nonlocal dynamics.