A Modified Operational Matrix Method for Solving System of Fractional Lotka-Volterra Equations

This paper examines the fractional Lotka-Volterra system, a cornerstone in the mathematical modeling of ecological and chemical processes. The primary objective is to introduce an innovative numerical technique for addressing nonlinear problems characterized by a nonsingular kernel. The proposed method is designed to be straightforward in implementation while minimizing computational effort and cost. To achieve this, the operational matrix method is refined and adapted. The study validates the effectiveness of this approach by applying it to various classes of fractional Lotka-Volterra systems. A thorough comparison is provided between the results obtained through this method and those generated by Mathematica’s built-in commands for integer-order derivatives. Additionally, the L₂-truncation error is evaluated to highlight the method’s enhanced accuracy and efficiency. The paper also addresses theoretical aspects, including the existence, uniqueness, error bounds, and convergence of the solutions, providing a robust foundation for the proposed approach.