Reconstruction of nonlinear integral inequalities associated with time scales calculus

Abstract

In this paper, we build up some generalizations of nonlinear integral inequalities and recreate the results of some Pachpatte's inequalities on time scales. We not just settle new estimated bounds of a particular class of nonlinear retarded dynamic inequalities, but additionally determine and unify continuous analogs alongside a subjective time scale T. We demonstrate applications of the treated inequalities to reflect the benefits of our work. The key effects will be proven by using the analysis procedure and the standard timescale comparison theorem technique.

A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

“…Numerical approximation The Atangana-Baleanu FO integral numerical approximation by imposing the Adams-Moulton rule is granted by [24] AB…”

“…However, in these models, the effects of long-range memories are neglected. Recently, mathematical systems with fractional order (FO) have become more worthy than classical systems as FO models provide the description of the memory effects [17][18][19][20][21][22][23][24][25][26][27][28][29]. Owolabi et al in [30] studied local and global stability of the fractional dynamical system of prey-predator with Holling type-II involving a time delay.…”