Hossein Jafari | University of South Africa (original) (raw)

Papers by Hossein Jafari

Research paper thumbnail of Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

Abstract and Applied Analysis, Mar 25, 2014

The local fractional Poisson equations in two independent variables that appear in mathematical p... more The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Research paper thumbnail of T-Stability Approach to the Homotopy Perturbation Method for Solving Fredholm Integral Equations

ABSTRACT The homotopy perturbation method is a powerful device for solving a wide variety of prob... more ABSTRACT The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for solving Fredholm integral equations.

Research paper thumbnail of Exact Solutions of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mi>v</mi><mi>a</mi><mi>r</mi><mi>p</mi><mi>h</mi><mi>i</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>b</mi><mi>f</mi><mn>4</mn></mrow></msup></mrow><annotation encoding="application/x-tex">{ varphi }^{ mathbf{4}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1279em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">p</span><span class="mord mathnormal">hi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9334em;"><span style="top:-3.1473em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ma</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">hb</span><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span><span class="mord mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span></span></span></span> Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods

Abstract and Applied Analysis, 2012

This paper obtains the exact solutions of the φ 4 equation. The Lie symmetry approach along with ... more This paper obtains the exact solutions of the φ 4 equation. The Lie symmetry approach along with the simplest equation method and the Exp-function method are used to obtain these solutions. As a simplest equation we have used the equation of Riccati in the simplest equation method. Exact solutions obtained are travelling wave solutions.

Research paper thumbnail of Optical Gaussons in Birefringent Fibers and DWDM Systems with Inter-Modal Dispersion

Romanian Reports in Physics, 2012

ABSTRACT This paper studies the optical solitons in birefringent fibers and DWDM systems in prese... more ABSTRACT This paper studies the optical solitons in birefringent fibers and DWDM systems in presence of log-law nonlinearity with inter-modal dispersion. The Gaussian ansatz is used to carry out theintegration of the governing equation. The exact solutions are obtained and the constraint conditions, for the existence of these Gaussons, fall out during the course of derivation ofthe solution. A brief discussion on Thirring solitons is also included.

Research paper thumbnail of The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative

Abstract and Applied Analysis, 2013

Research paper thumbnail of Relation of Biogenic Amines and Bacterial Changes in Ice-Stored Southern Caspian Kutum (Rutilus Frisii Kutum)

Journal of Food Biochemistry, Jul 4, 2007

The biogenic amine (putrescine, cadaverine, histamine and tyramine) content of whole Southern Cas... more The biogenic amine (putrescine, cadaverine, histamine and tyramine) content of whole Southern Caspian Kutum (Rutilus frisii kutum) and related bacterial changes (Pseudomonas spp., psychrotrophic and mesophilic counts) were monitored during ice storage for a period of 18 days (0, 3, 6, 9, 12, 15 and 18). Levels of putrescine, cadaverine and bacterial loads increased (P < 0.05) during storage, but histamine and tyramine were not detected in any of the tested samples. Initial concentrations of putrescine and cadaverine were 0.24 and 0.07 mm/kg, and finally reached 5.27 and 4.21 mg/kg, respectively. Correlations were found between putrescine and psychrotrophs, and between cadaverine and pseudomonads. The putrescine and cadaverine content of

Research paper thumbnail of Application of Homotopy-Perturbation Method for Solving Gas Dynamics Equation

In this paper applies the He's homotopy perturbation method (HPM)to obtaining solution of nonline... more In this paper applies the He's homotopy perturbation method (HPM)to obtaining solution of nonlinear dynamic model.The nonlinear considered model is the Gas Dynamics equation.

Research paper thumbnail of Homotopy Perturbation Pade Technique for Solving Fractional Riccati Differential Equations

International Journal of Nonlinear Sciences and Numerical Simulation, 2010

Research paper thumbnail of Boundary value problems for fractional diffusion-wave equation

Australian Journal of Mathematical Analysis and Applications, 2006

The fractional di usion equation is solved for di erent boundary value problems, these being abso... more The fractional di usion equation is solved for di erent boundary value problems, these being absorbing and re ecting boundaries in half-space and in a box. Thereby, the method of images and the Fourier-Laplace transformation technique are employed. The separation of variables is studied for a fractional di usion equation with a potential term, describing a generalisation of an escape problem through a uctuating bottleneck. The results lead to a further understanding of the fractional framework in the description of complex systems which exhibit anomalous di usion.

Research paper thumbnail of On a numerical solution for fractional differential equation within B-spline operational matrix

Icfda 14 International Conference on Fractional Differentiation and Its Applications 2014, Jun 1, 2014

Research paper thumbnail of An algorithm for solving a system of linear ordinary differential equations

Abstract A number of problems in science and engineering are modeled in terms of a system of ordi... more Abstract A number of problems in science and engineering are modeled in terms of a system of ordinary differential equations. In this paper, an algorithm for solving a system of linear ordinary differential equations (ODE) has been presented, which converts a system of ...

Research paper thumbnail of Convergence of Homotopy perturbation method for solving integral equations

The aim of this paper is convergence study of homotopy perturbation method (HPM) for solving inte... more The aim of this paper is convergence study of homotopy perturbation method (HPM) for solving integral equations in general case. The homotopy perturbation method is a powerful device for solving a wide variety of problems. Using the homotopy perturbation method, it is possible to find the exact solution or an approximate solution of the problem. Some illustrative examples are presented.

Research paper thumbnail of Homotopy Analysis Method for Solving KDV Equations

A scheme is developed for the numerical study of the Korteweg-de Vries (KdV) and the Korteweg-de ... more A scheme is developed for the numerical study of the Korteweg-de Vries (KdV) and the Korteweg-de Vries Burgers (KdVB) equations with initial conditions by a homotopy approach. Numerical solutions obtained by homotopy analysis method are compared with exact solution. The comparison shows that the obtained solutions are in excellent agreement. Full text

Research paper thumbnail of Numerical solutions of telegraph and Laplace equations on Cantor sets using local fractional Laplace decomposition method

Research paper thumbnail of Adomian Decomposition: A tool for solving fractional differential equations

Journal of Mathematical Analysis and Applications

Research paper thumbnail of The Homotopy Analysis Method For Higher Dimensional Boundary Value Problems of Variable Coefficients

Numerical Methods for Partial Differential Equations

Research paper thumbnail of Approximate Analytical Solution of a Coupled System of Fractional Partial Differential Equations by Bernstein Polynomials

International Journal of Applied and Computational Mathematics, 2015

In this paper, we produce numerical solution for a coupled system of partial differential equatio... more In this paper, we produce numerical solution for a coupled system of partial differential equations of fractional order (PDEFO) by the help of Bernstein polynomials. This method reduces the coupled system of PDEFO to a system of algebraic equations which is simple in handling and gives us good results. The accuracy of the results are examined by examples.

Research paper thumbnail of Homotopy analysis method for solving Abel differential equation of fractional order

Research paper thumbnail of Numerical Solution of Non-linear Riccati Differential Equations with Fractional Order

International Journal of Nonlinear Sciences and Numerical Simulation, 2010

Research paper thumbnail of Fractional Lie group method of the time-fractional Boussinesq equation

Nonlinear Dynamics, 2015

ABSTRACT Finding the symmetries of the nonlinear fractional differential equations is a topic whi... more ABSTRACT Finding the symmetries of the nonlinear fractional differential equations is a topic which has many applications in various fields of science and engineering. In this manuscript, firstly, we are interested in finding the Lie point symmetries of the time-fractional Boussinesq equation. After that, by using the infinitesimal generators, we determine their corresponding invariant solutions.

Research paper thumbnail of Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

Abstract and Applied Analysis, Mar 25, 2014

The local fractional Poisson equations in two independent variables that appear in mathematical p... more The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Research paper thumbnail of T-Stability Approach to the Homotopy Perturbation Method for Solving Fredholm Integral Equations

ABSTRACT The homotopy perturbation method is a powerful device for solving a wide variety of prob... more ABSTRACT The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for solving Fredholm integral equations.

Research paper thumbnail of Exact Solutions of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mi>v</mi><mi>a</mi><mi>r</mi><mi>p</mi><mi>h</mi><mi>i</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>b</mi><mi>f</mi><mn>4</mn></mrow></msup></mrow><annotation encoding="application/x-tex">{ varphi }^{ mathbf{4}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1279em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">p</span><span class="mord mathnormal">hi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9334em;"><span style="top:-3.1473em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ma</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">hb</span><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span><span class="mord mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span></span></span></span> Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods

Abstract and Applied Analysis, 2012

This paper obtains the exact solutions of the φ 4 equation. The Lie symmetry approach along with ... more This paper obtains the exact solutions of the φ 4 equation. The Lie symmetry approach along with the simplest equation method and the Exp-function method are used to obtain these solutions. As a simplest equation we have used the equation of Riccati in the simplest equation method. Exact solutions obtained are travelling wave solutions.

Research paper thumbnail of Optical Gaussons in Birefringent Fibers and DWDM Systems with Inter-Modal Dispersion

Romanian Reports in Physics, 2012

ABSTRACT This paper studies the optical solitons in birefringent fibers and DWDM systems in prese... more ABSTRACT This paper studies the optical solitons in birefringent fibers and DWDM systems in presence of log-law nonlinearity with inter-modal dispersion. The Gaussian ansatz is used to carry out theintegration of the governing equation. The exact solutions are obtained and the constraint conditions, for the existence of these Gaussons, fall out during the course of derivation ofthe solution. A brief discussion on Thirring solitons is also included.

Research paper thumbnail of The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative

Abstract and Applied Analysis, 2013

Research paper thumbnail of Relation of Biogenic Amines and Bacterial Changes in Ice-Stored Southern Caspian Kutum (Rutilus Frisii Kutum)

Journal of Food Biochemistry, Jul 4, 2007

The biogenic amine (putrescine, cadaverine, histamine and tyramine) content of whole Southern Cas... more The biogenic amine (putrescine, cadaverine, histamine and tyramine) content of whole Southern Caspian Kutum (Rutilus frisii kutum) and related bacterial changes (Pseudomonas spp., psychrotrophic and mesophilic counts) were monitored during ice storage for a period of 18 days (0, 3, 6, 9, 12, 15 and 18). Levels of putrescine, cadaverine and bacterial loads increased (P < 0.05) during storage, but histamine and tyramine were not detected in any of the tested samples. Initial concentrations of putrescine and cadaverine were 0.24 and 0.07 mm/kg, and finally reached 5.27 and 4.21 mg/kg, respectively. Correlations were found between putrescine and psychrotrophs, and between cadaverine and pseudomonads. The putrescine and cadaverine content of

Research paper thumbnail of Application of Homotopy-Perturbation Method for Solving Gas Dynamics Equation

In this paper applies the He's homotopy perturbation method (HPM)to obtaining solution of nonline... more In this paper applies the He's homotopy perturbation method (HPM)to obtaining solution of nonlinear dynamic model.The nonlinear considered model is the Gas Dynamics equation.

Research paper thumbnail of Homotopy Perturbation Pade Technique for Solving Fractional Riccati Differential Equations

International Journal of Nonlinear Sciences and Numerical Simulation, 2010

Research paper thumbnail of Boundary value problems for fractional diffusion-wave equation

Australian Journal of Mathematical Analysis and Applications, 2006

The fractional di usion equation is solved for di erent boundary value problems, these being abso... more The fractional di usion equation is solved for di erent boundary value problems, these being absorbing and re ecting boundaries in half-space and in a box. Thereby, the method of images and the Fourier-Laplace transformation technique are employed. The separation of variables is studied for a fractional di usion equation with a potential term, describing a generalisation of an escape problem through a uctuating bottleneck. The results lead to a further understanding of the fractional framework in the description of complex systems which exhibit anomalous di usion.

Research paper thumbnail of On a numerical solution for fractional differential equation within B-spline operational matrix

Icfda 14 International Conference on Fractional Differentiation and Its Applications 2014, Jun 1, 2014

Research paper thumbnail of An algorithm for solving a system of linear ordinary differential equations

Abstract A number of problems in science and engineering are modeled in terms of a system of ordi... more Abstract A number of problems in science and engineering are modeled in terms of a system of ordinary differential equations. In this paper, an algorithm for solving a system of linear ordinary differential equations (ODE) has been presented, which converts a system of ...

Research paper thumbnail of Convergence of Homotopy perturbation method for solving integral equations

The aim of this paper is convergence study of homotopy perturbation method (HPM) for solving inte... more The aim of this paper is convergence study of homotopy perturbation method (HPM) for solving integral equations in general case. The homotopy perturbation method is a powerful device for solving a wide variety of problems. Using the homotopy perturbation method, it is possible to find the exact solution or an approximate solution of the problem. Some illustrative examples are presented.

Research paper thumbnail of Homotopy Analysis Method for Solving KDV Equations

A scheme is developed for the numerical study of the Korteweg-de Vries (KdV) and the Korteweg-de ... more A scheme is developed for the numerical study of the Korteweg-de Vries (KdV) and the Korteweg-de Vries Burgers (KdVB) equations with initial conditions by a homotopy approach. Numerical solutions obtained by homotopy analysis method are compared with exact solution. The comparison shows that the obtained solutions are in excellent agreement. Full text

Research paper thumbnail of Numerical solutions of telegraph and Laplace equations on Cantor sets using local fractional Laplace decomposition method

Research paper thumbnail of Adomian Decomposition: A tool for solving fractional differential equations

Journal of Mathematical Analysis and Applications

Research paper thumbnail of The Homotopy Analysis Method For Higher Dimensional Boundary Value Problems of Variable Coefficients

Numerical Methods for Partial Differential Equations

Research paper thumbnail of Approximate Analytical Solution of a Coupled System of Fractional Partial Differential Equations by Bernstein Polynomials

International Journal of Applied and Computational Mathematics, 2015

In this paper, we produce numerical solution for a coupled system of partial differential equatio... more In this paper, we produce numerical solution for a coupled system of partial differential equations of fractional order (PDEFO) by the help of Bernstein polynomials. This method reduces the coupled system of PDEFO to a system of algebraic equations which is simple in handling and gives us good results. The accuracy of the results are examined by examples.

Research paper thumbnail of Homotopy analysis method for solving Abel differential equation of fractional order

Research paper thumbnail of Numerical Solution of Non-linear Riccati Differential Equations with Fractional Order

International Journal of Nonlinear Sciences and Numerical Simulation, 2010

Research paper thumbnail of Fractional Lie group method of the time-fractional Boussinesq equation

Nonlinear Dynamics, 2015

ABSTRACT Finding the symmetries of the nonlinear fractional differential equations is a topic whi... more ABSTRACT Finding the symmetries of the nonlinear fractional differential equations is a topic which has many applications in various fields of science and engineering. In this manuscript, firstly, we are interested in finding the Lie point symmetries of the time-fractional Boussinesq equation. After that, by using the infinitesimal generators, we determine their corresponding invariant solutions.