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...

In this article, we conjugate time marching schemes with Finite Differences splittings into low and high modes in order to build fully explicit methods with enhanced temporal stability for the numerical solutions of PDEs. The main idea is to apply explicit schemes with less restrictive stability conditions to the linear term of the high modes equation, in order that the allowed time step for th...

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed ‘Non-linear grid system’ is presented. The linear terms in Navier-Stokes equation are solved by CrankNicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Split...

A comparison between different numerical methods which are used to solve cross flow model in multicomponent membrane gas separation is studied. Considering cross flow model, numerical methods such as Bogacki-Shampine method, Dormand-Prince method, Adams-Bashforth-Moulton method, numerical differentiation formulas, modified Rosenbrock formula of order 2, Trapezoidal rule with free interpolant an...

We introduce new projective versions of second-order accurate Runge-Kutta and Adams-Bashforth methods, and demonstrate their use as outer integrators in solving stiff differential systems. An important outcome is that the new outer integrators, when combined with an inner telescopic projective integrator, can result in fully explicit methods with adaptive outer step size selection and solution ...

In this paper we concern with asymptotic stability, synchronization control and numerical solution of incommensurate order fractional Shimizu–Morioka dynamical system. Firstly we prove the existence and uniqueness of the solutions via a new theorem. After finding steady–state points, we obtain necessary and sufficient conditions for the asymptotic stability of the Shimizu–Morioka system. We als...

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...

A third-order in time numerical IMEX-type algorithm for the StokesDarcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel third-order Adams-Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams-Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy compon...

HIV, like many other infections, is a severe and lethal infection. Fractal-fractional operators are frequently used in modeling numerous physical processes the current decade. These provide better dynamics of mathematical model because these generalization integer fractional-order operators. This paper aims to study HIV during primary infection by fractal-fractional Atangana–Baleanu (AB) The su...

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 ...