In this article, we investigate the utilization of Riemann–Liouville’s fractional integral and Caputo derivative in application Optimal Auxiliary Function Method (OAFM). The extended OAFM is employed to analyze non-linear coupled ITO systems KDV systems, which feature equations a order time. We compare results obtained for system with those derived from Homotopy Perturbation (HPM) New Iterative...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

In this work, we consider two-dimensional linear and nonlinear Fredholm integral equations of the first kind. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method is used to find a solution to the equation. The application of this method is based upon converting the first kind of equation to the second kind by applying...

We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method. We use this method for solving Generalized Time-space Fractional Schrödinger equation. The fractional derivative is described in Caputo sense. The proposed scheme finds the solution without any discritization, ...

in oil industry, spontaneous imbibition is an important phenomenon in recovery from fractured reservoirs which can be defined as spontaneous uptake of a wetting fluid into a porous solid. spontaneous imbibition involves both cocurrent and countercurrent flows. when a matrix block is partially covered by water, oil recovery is dominated by cocurrent imbibition i.e. the production of non wetting ...

The coupled system of non-linear second-order reaction differential equation in basic enzyme reaction is formulated and closed analytical expressions for substrate and product concentrations are presented. Approximate analytical method (He’s Homotopy perturbation method) is used to solve the coupled non-linear differential equations containing a non-linear term related to enzymatic reaction. Cl...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

An approximate analytical solution of the Balitsky–Kovchegov (BK) equation using homotopy perturbation method (HPM) is suggested in this work. We carried out our work perturbative Quantum Chromodynamics (QCD) (pQCD) dipole picture deep inelastic scattering (DIS). The BK momentum space with some change variables and truncation Balitsky–Fadin–Kuraev–Lipatov (BFKL) kernel can be reduced to Fisher–...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

In this paper, the problem of laminar nanofluid flow in a semi-porous channel is investigated analytically using Homotopy Perturbation Method (HPM). This problem is in the presence of transverse magnetic field. Here, it has been attempted to show the capabilities and wide-range applications of the Homotopy Perturbation Method in comparison with the numerical method in solving such problems. The...