The adaptation of fractional calculus (FC) in biological mathematical model takes the research in the area of the public health to a new level. The fractional definitions and related mathematical tools have had a significant impact on biological models analysis. The main goal of this paper is to examine the dynamical behavior of a predator–prey model under Caputo derivative. We analyze some special results such as convergence analysis, stability and operational matrix for the proposed Caputo model. For solution of the model, we present a new numerical technique-based Laguerre wavelet. In addition, we graphically compare the numerical results obtained using Laguerre wavelets and Lagrange polynomial interpolation.