An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials

This article extends a spectral collocation approach based on Lucas polynomials to numerically solve the integrodifferential equations of both Volterra and Fredholm types for multi–higher fractional order in the Caputo sense under the mixed conditions. The new approach focusses on using a matrix strategy to convert the supplied equation with conditions into an algebraic linear system of equations with unknown Lucas coefficients. The coefficients of the presumed solution are determined by the solution of this system. The Lucas coefficients are used to track how the solutions behave. This method is attractive for computation, and usage examples and explanations are provided. Additionally, certain examples are provided to demonstrate the method’s accuracy, and the least-squares error technique is employed to reduce error terms inside the designated domain. Because of this, Python is used to write most general programs.