Spectral Collocation Approach via Normalized Shifted Jacobi Polynomials for the Nonlinear Lane-Emden Equation with Fractal-Fractional Derivative

Herein, we adduce, analyze, and come up with spectral collocation procedures to iron out a specific class of nonlinear singular Lane–Emden (LE) equations generalized Caputo derivatives that appear in the study astronomical objects. The offered solution is approximated as truncated series normalized shifted Jacobi polynomials under assumption exact an element L2. method used solver obtain unknown expansion coefficients. roots are nodes. Our solutions can easily be generalization classical LE equation, by obtaining numerical based on new parameters, fixing these parameters case, equation. We provide meticulous convergence analysis demonstrate rapid truncation error concerning number retained modes. Numerical examples show effectiveness applicability method. primary benefits suggested approach significantly reduce complexity underlying differential equation solving system algebraic done quickly accurately using Newton’s vanishing initial guesses.