A MODIFIED OPERATIONAL MATRIX METHOD FOR INVESTIGATING THE DYNAMICS FRACTIONAL LOTKA-VOLTERRA TYPE MODEL

In this paper, we explore the dynamics of the well-established Lotka-Volterra equations, which serve as fundamental models in the mathematical rep-resentation of ecological and chemical systems. Our focus is on presenting a novel numerical method for solving nonlinear problems with a singular kernel. Our aim is to develop a novel numerical method that is easy to implement and reduces computational time and cost. We achieve this goal by modifying the operational matrix method. Through our study, we demonstrate the efficacy of this numerical approach and illustrate its application in solving several classes of Lotka-Volterra equations. We provide comprehensive comparisons with the results generated by built-in commands in Mathematica when dealing with integer derivatives. Additionally, we compute the L₂-truncation error to showcase the superior effectiveness and accuracy of our approach. Furthermore, we discuss some theoretical results such as the existence, uniqueness, error estimates, and convergence of the solution.