In this paper, a fractional order model based on the management of waste plastic in ocean (FO-MWPO) is numerically investigated. The mathematical form FO-MWPO categorized into three components, plastic, Marine debris, and recycling. stochastic numerical solvers using Levenberg-Marquardt backpropagation neural networks (LMQBP-NNs) have been applied to present solutions system. competency method ...

The purposes of this work are to study the $L^{2}$-stability a Navier-Stokes type model for non-stationary flow in porous media proposed by Hsu and Cheng 1989 develop Lagrange-Galerkin scheme with Adams-Bashforth method solve that numerically.The stability estimate is obtained thanks presence nonlinear drag force term which corresponds Forchheimer term. We derive extending idea characteristics ...

This paper constructs multirate linear multistep time discretizations based on Adams-Bashforth methods. These methods are aimed at solving conservation laws and allow different timesteps to be used in different parts of the spatial domain. The proposed family of discretizations is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL co...

In this chapter, some real-life model problems that can be formulated as ordinary differential equations (ODEs) are introduced and numerically studied. These models are the variable-order fractional Hodgkin–Huxley model of neuronal excitation (VOFHHM) and other models with the variable-order fractional (VOF) time delay, such as the 4year life cycle of a population of lemmings model, the enzyme ...

Assuming that the population remains small, one can truncate at given values of n1 and n2 to yield a finite set of differential equations. For an initial condition, we take the population to be zero, that is, ρ1,1,1,1 = 1 with all other elements of the density matrix set to zero. Eq. A.6 can then be solved numerically (we used the Adams-Moulton-Bashforth procedure) until a steady state is reach...

In this study, we propose new illustrative and effective modeling to point out the behaviors of Hepatitis-B virus (Hepatitis-B). Not only do consider mathematical modeling, equilibria, stabilities, existence–uniqueness analysis model, but also, make numerical simulations by using Adams–Bashforth scheme. However, apply parameter estimation method determine our model parameters find curve that be...

We investigate the long time behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equation in a periodic box: 3ω − 4ω + ω 2k +∇(2ψ − ψ) · ∇(2ω − ω)− ν∆ω = f, −∆ψ = ω. The scheme is a combination of a 2nd order in time backward-differentiation (BDF) and a special explicit Adams-Bashforth treatment of the advection term. Therefore only a linear constant coeffic...

The current manuscript describes the dynamics of a fractional mathematical model serial killing under Mittag–Leffler kernel. Using fixed point theory approach, we present qualitative analysis problem and establish result that ensures existence at least one solution. Ulam’s stability given is presented by using nonlinear concepts. iterative fractional-order Adams–Bashforth approach being used to...

Abstract This paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator prey act as agents in an ecosystem this simulation. We focus on order Atangana–Baleanu operator the sense Liouville–Caputo. Due nonlocality method, generated by using another FO derivative developed kernel based generalized Mittag-Leffler function. Two fractio...