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This paper aims to develop accurate novel collocation techniques for solving a fractional fractional-order Lotka–Volterra (LV) predator–prey model. This type of equation has a wide variety of applications in biology to simulate the interaction between two different species. The fractional-order operator is defined in the Caputo sense. We introduce some new polynomials for solving this type of equation named the Morgan-Voyce polynomials. These new techniques named direct and quasilinear Morgan-Voyce techniques are presented and then used to solve the LV system revealing some of the new features of the model. Some of the advantages of the application of these techniques are that they are straightforward along with high accuracy. Detailed error and convergence analysis for the proposed methods are provided revealing the upper bound for these techniques. To test the accuracy of the proposed methods …