In this article, an efficient modification of the Picard iteration method for solving the multispecies Lotka-Volterra modelss (MLVMs) is firstly proposed. Then the convergence and stability of the modified method are discussed. In order to indicate the efficiency of the modified method, three cases of the MLVMs are given. The obtained results evidence that the developed approach is a useful semi-analytical scheme for the solution of the MLVMs.

This study examines the memory effect on predator-prey interactions in the face of global warming, employing a fear function with a Holling type II function to characterize the consumer prey and predator species. The effect of global warming on both prey and predators was studied using the exponential decay function. The system’s equilibria are determined, and the system’s stability is established around the equilibrium points. A series of numerical simulations are done to evaluate the theoretical component of the work and show the impacts of global warming, anxiety, and fractional order on our model’s behavior.

In this paper first we present some new identities by using the notions of quantum integrals and derivatives which allows us to obtain new quantum Simpson’s and quantum Newton’s type inequalities for differentiable convex functions by using the q_{x}-quantum integral and q^{y}-quantum integral. In particular, this paper generalises and extends previous results obtained by the various authors in the field of quantum and classical integral inequalities.