A STUDY ON FRACTIONAL LANE–EMDEN EQUATION OF ASTROPHYSICS AS THERMAL EXPLOSIONS USING CHEBYSHEV WAVELET METHOD

Thermal explosions in astrophysical systems are crucial for understanding stellar evolution and dynamics. The fractional Lane–Emden equation is a key mathematical tool for modeling these explosions, providing insight into the thermodynamic processes within stellar interiors. Knowledge of such equations is significant because they quantify the temperature field and transport of energy within self-gravitating systems. A notable challenge in solving these equations arises from the singularity at $ x=0 $, which requires careful numerical handling. Standard analytical methods may not give exact solutions to fractional-order models, necessitating effective numerical solutions. In this paper, we use the second-kind Chebyshev wavelet approximation to solve the fractional Lane–Emden equation effectively. This method utilizes orthogonality and the wavelet operational matrices to convert the original problem into algebraic equations, significantly reducing the computational burden. Numerical experiments confirm that the presented technique is not only efficient and precise but also has the least computational cost compared to traditional numerical methods. Therefore, it makes it highly suitable for solving other complex fractional models in astrophysics.