In this article, we study the fractional SIR epidemic model with Atangana–Baleanu–Caputo operator. We explore properties and applicability of ZZ transformation on operator as transform derivative. This is an application two power methods. obtain a special solution homotopy perturbation method (HPM) combined scheme; then present problem existence solution, also apply new to solving ABC The solut...

In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The res...

In this paper, the restarted Adomian decomposition method (RADM) is presented to establish an accurate approximate analytical solutions for Duffingvan der Pol (DVP) differential equation. The Lindsted’s method (LM) is used to compare the solutions of the RADM with those obtained using the Adomian decomposition method (ADM). The numerical results show that the RADM in identical conditions gives ...

a new modified adomian decomposition method (adm) is utilized to obtain an analytical solution for buckling of the nanocantilever actuators immersed in liquid electrolytes. the nanoactuators in electrolytes are subject to different nonlinear forces including ionic concentration, van der waals, external voltage and electrochemical forces. the duan–rach modified adomian decomposition method is ut...

Due to wide range of interest in use of bioeconomic models to gain insight into the scientific management of renewable resources like fisheries and forestry, homotopy perturbation method is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting. The results are compared with the results obtained by Adomian decomposition method. The ...

In this study, two numerical methods—the variational iteration transform method (VITM) and the Adomian decomposition (ADM) method—were used to solve second- fourth-order fractional Boussinesq equations. Both methods are helpful in approximating non-linear problems effectively, easily, accurately. The Atangana–Baleanu operator ZZ were utilized derive solutions for equation. Two examples discusse...

This work aims at a new semi-analytical technique called the Adomian decomposition method for analysis of time-fractional Emden–Fowler equations. The Laplace transformation and iterative are implemented to obtain result given models. suggested has edge over other methods, as it does not need extra materials calculations. presented validity is demonstrated by examining four mathematical Due stra...

This work suggests a new analytical technique called the fractional homotopy analysis transform method (FHATM) for solving nonlinear homogeneous andnonhomogeneous time-fractional gas dynamics equations. The FHATM is an innovative adjustment in Laplace transform algorithm (LTA) and makes the calculation much simpler. The proposed technique solves the nonlinear problems without using Adomian poly...

In this article, we use the homotopy perturbation method and Adomian decomposition with Yang transformation to discover analytical solution time-fractional coupled Schrödinger–KdV equation. Caputo sense, fractional derivatives are described. A convergent series is used calculate solutions of PDEs. Analytical results achieved applying techniques numerically calculated represented in form tables ...