Naeem Faraz

The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet

The effects of variable viscosity and thermal conductivity on the flow and heat transfer in a laminar liquid film on a horizontal shrinking/stretching sheet are analyzed. The similarity transformation reduces the time independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The resulting five-parameter problem is solved by the homotopy perturbation method. The results are presented graphically to interpret various physical parameters appearing in the problem.

New soliton solutions of the generalized Zakharov equations using He’s variational approach

Abstract In this paper, we obtain new soliton solutions of the generalized Zakharov equations by the well-known He’s variational approach. The condition for continuation of the new solitary solution is obtained.

Fractional variational iteration method for fractional initial-boundary value problems arising in the application of nonlinear science

In this paper, we suggest a fractional functional for the variational iteration method to solve the linear and nonlinear fractional order partial differential equations with fractional order initial and boundary conditions by using the modified Riemann-Liouville fractional derivative proposed by G. Jumarie. Fractional order Lagrange multiplier has been considered. Solution has been plotted for different values of @a.

Exp‐function method for solitary and periodic solutions of Fitzhugh‐Nagumo equation

Purpose – The purpose of this paper is to apply exp‐function method to construct generalized solitary and periodic solutions of Fitzhugh‐Nagumo equation, which plays a very important role in mathematical physics and engineering sciences.Design/methodology/approach – The authors apply exp‐function method to construct generalized solitary and periodic solutions of Fitzhugh‐Nagumo equation.Findings – Numerical results clearly indicate the reliability and efficiency of the proposed exp‐function method. The suggested algorithm is quite efficient and is practically well suited for use in these problems.Originality/value – In this paper, the authors applied the exp‐function method to obtain solutions of the Fitzhugh‐Nagumo equation and show that the exp‐function method gives more realistic solutions without disturbing the basic physics of the physical problems.

A new fractional analytical approach via a modified Riemann–Liouville derivative

Abstract This work suggests a new analytical technique called the fractional homotopy perturbation method (FHPM) for solving fractional differential equations of any fractional order. This method is based on He’s homotopy perturbation method and the modified Riemann–Liouville derivative. The fractional differential equations are described in Jumarie’s sense. The results from introducing a modified Riemann–Liouville derivative in the cases studied show the high accuracy, simplicity and efficiency of the approach.

A Series Solution of the Long Porous Slider

A series solution of the long porous slider problem where fluid is injected through the porous bottom is obtained using the homotopy perturbation method (HPM). Similarity solutions of coupled nonlinear ordinary differential equations resulting from the momentum equation are obtained. Numerical results are obtained and discussed for different values of Reynolds number of the velocity field. The numerical results demonstrate the validity and applicability of the method.

A New Approach to Van der Pol’s Oscillator Problem

In this paper, we will consider the Laplace decomposition method (LDM) for finding series solutions of nonlinear oscillator differential equations. The equations are Laplace transformed and the nonlinear terms are represented by He’s polynomials. The solutions are compared with the numerical (fourth-order Runge-Kutta) solution and the solution obtained by the Adomian decomposition method. The suggested algorithm is more efficient and easier to handle as compared to the numerical method. The results illustrate that LDM is an appropriate method in solving the highly nonlinear equations.

An Alternative Approach to Differential-Difference Equations Using the Variational Iteration Method

Although a variational iteration algorithm was proposed by Yildirim (Math. Prob. Eng. 2008 (2008), Article ID 869614) that successfully solves differential-difference equations, the method involves some repeated and unnecessary iterations in each step. An alternative iteration algorithm (variational iteration algorithm-II) is constructed in this paper that overcomes this shortcoming and promises to provide a universal mathematical tool for many differential-difference equations.

An efficient new perturbative Laplace method for space-time fractional telegraph equations

In this paper, we propose a new technique for solving space-time fractional telegraph equations. This method is based on perturbation theory and the Laplace transformation. Fractional Taylor series and fractional initial conditions have been introduced. However, all the previous works avoid the term of fractional initial conditions in the space-time telegraph equations. The results of introducing fractional order initial conditions and the Laplace transform for the studied cases show the high accuracy, simplicity and efficiency of the approach.

Heat Transfer Analysis on the Magnetohydrodynamic Flow of a Non- Newtonian Fluid in the Presence of Thermal Radiation: An Analytic Solution

In this paper, a two-dimensional, steady magnetohydrodynamic flow and heat transfer analysis of a non-Newtonian fluid in a channel with a constant wall temperature are considered in the presence of thermal radiation. The steady Navier-Stokes equations are reduced to nonlinear ordinary differential equations by using similarity variables. The homotopy perturbation method is used to solve the nonlinear ordinary differential equations. The effects of the pertinent parameters on the velocity and temperature field are discussed