A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet method

This study aims to explore the Legendre wavelet method for numerically solving neutral fractional differential equations with constant delay using fractional derivatives in the Hilfer sense. By utilizing the function approximation and properties of the Legendre wavelet, we derive an approximate solution for the given dynamical system, reducing the neutral Hilfer fractional derivatives with constant delay to algebraic expressions. Additionally, we present a convergence analysis and error estimation for the truncated Legendre wavelet expansion in the context of the proposed method. To verify the effectiveness of the approach, several numerical examples are provided, along with graphical illustrations that clearly demonstrate the applicability and accuracy of the method, thereby supporting the validity of the theoretical results.