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2010
1
1
59
Huang Method for Solving Fully Fuzzy Linear System of Equations
Huang Method for Solving Fully Fuzzy Linear System of Equations
en
en
Recently, solving fuzzy versions of linear system of equations has been attracted many interests. As we
know, unfortunately any practical method for finding a general solution of these systems is not at hand.
In this paper, we concentrate on solving fully fuzzy linear system of equations and propose Huang
method for computing a nonnegative solution of the fully fuzzy linear system of equations.
1
5
S. H.
Nasseri
F.
Zahmatkesh
Fuzzy arithmetic
Fully fuzzy linear system
Fuzzy number
Huang method.
Article.1.pdf
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J. Abaffy, E. Spedicato, ABS Projection Algorithms: Mathematical Techniques for Linear and nonlinear Equations, John Wiley & Sons, New York (1989)
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M. Dehghan, B. Hashemi, M. Ghatee, Mehdi Computational methods for solving fully fuzzy linear systems, Appl. Math. Comput., 179 (2006), 328-343
##[3]
M. Dehghan, B. Hashemi, Solution of the fully fuzzy linear systems using the decomposition procedure, Appl. Math. Comput., 182 (2006), 1568-1580
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D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York (1980)
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S. H. Nasseri, M. Khorramizadeh, A new method for solving fuzzy linear systems, Int. J. Appl. Math., 20 (2007), 507-516
##[6]
S. H. Nasseri, M. Matinfar, Z. Kheiri, Grevilles method for the fully fuzzy linear system of equations, Adv. Fuzzy Sets Syst., 4 (2009), 301-311
##[7]
S. H. Nasseri, M. Sohrabi, E. Ardil, Solving fully fuzzy linear systems by use of a certain decomposition of the coefficient matrix, Int. J. Comput. Math. Sci., 2 (2008), 140-142
##[8]
E. Spedicato, E. Bodon, A. Del Popolo, N. Mahdavi-Amiri, ABS methods and ABSPACK for linear systems and optimization, 4OR, 1 (2003), 51-66
]
Acceptance Single Sampling Plan by Using of Poisson Distribution
Acceptance Single Sampling Plan by Using of Poisson Distribution
en
en
This purpose of this paper is to present the acceptance single sampling plan when the fraction of
nonconforming items is a fuzzy number and being modeled based on the fuzzy Poisson distribution. We have
shown that the operating characteristic (OC) curves of the plan are like a band having high and low bounds
whose width depends on the ambiguity proportion parameter in the lot when that sample size and acceptance
numbers is fixed. Finally we completed discuss opinion by a numerical example. And then we compared the
OC bands of using of binomial with the OC bands of using of Poisson distribution.
6
13
E.
Baloui Jamkhaneh
B.
Sadeghpour-Gildeh
Gh.
Yari
Statistical quality control
Acceptance single sampling
Fuzzy number.
Article.2.pdf
[
[1]
J. J. Buckley, Fuzzy Probabilities: New Approach and Applications, Physica-Verlag, Heidelberg (2003)
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J. J. Buckley, Fuzzy Probability and Statistics, Springer-Verlag, Berlin-Heidelberg (2006)
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D. Dubis, H. Prade, Operations on fuzzy numbers, Int J Syst Sci., 9 (1978), 613-626
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B. P. M. Duate, P. M. Saraiva, An optimization‐based approach for designing attribute acceptance sampling plans, Int. journal of quality & reliability management, 25 (2008), 824-841
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P. Grzegorzewski, Acceptance Sampling Plans by Attributes with Fuzzy Risks and Quality Levels, Frontiers in Statistical Quality Control, 6 (2001), 36-46
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P. Grzegorzewski, A Soft Design of Acceptance Sampling Plans by Variables, Technologies for Constructing Intelligent Systems, 2 (2002), 275-286
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A. Kanagawa, H. Ohta, A design for single sampling attribute plan based on fuzzy sets theory, Fuzzy Sets and Systems, 37 (1990), 173-181
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D. C. Montgomery, Introduction to Statistical Quality Control, John Wiley & Sons, New York (1991)
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F. Tamaki, A. Kanagawa, H. Ohta , A fuzzy design of sampling inspection plans by attributes, Japanese J. Fuzzy Theory Systems, 3 (1991), 315-327
]
Numerical Solution of 12th Order Boundary Value Problems by Using Homotopy Perturbation Method
Numerical Solution of 12th Order Boundary Value Problems by Using Homotopy Perturbation Method
en
en
In this paper, a homotopy-perturbation method (HPM) [1-6, 26-28] is used to solve both linear and
nonlinear Nth boundary value problems with two point boundary conditions for ninth-order, tenth-order
and twelfth-order. By applying (HPM) on three examples the numerical results are compared with the
exact solution, to show effectiveness and accuracy of the method.
14
27
Mohamed I. A.
Othman
A. M. S.
Mahdy
R. M.
Farouk
HPM
linear and non-linear problems
boundary value problem
Approximate solution
Article.3.pdf
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[1]
A. Golbabai, M. Javidi, Application of homotopy perturbation method for solving eighth-order boundary value problems, Appl. Math. Comput., 191 (2007), 334-346
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J.-H. He, A coupling method of a homotopy technique and a perturbation technique for nonlinear problems, Int. J. Non-Linear Mech., 35 (2000), 37-43
##[3]
J.-H. He, The homotopy perturbation method for non-linear oscillators with discontinuities, Appl. Math. Comput., 151 (2004), 287-292
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J.-H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals, 26 (2005), 695-700
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J.-H. He, Asymptotology by homotopy perturbation method, Appl. Math. Comput., 156 (2004), 591-596
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J.-H. He, Homotopy perturbation method for solving boundary problems, Phys. Lett. A, 350 (2006), 87-88
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J.-H. He, Limit cycle and bifurcation of nonlinear problems, Chaos Solitons Fractals, 26 (2005), 827-833
##[8]
S. Abbasbandy, Iterated Hes homotopy perturbation method for quadratic Riccati differential equation, Appl. Math. Comput., 175 (2006), 581-589
##[9]
P. D. Ariel, T. Hayat, S. Asghar, Homotopy perturbation method and axisymmetric flow over a stretching sheet, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 399-406
##[10]
D. D. Ganji, A. Sadighi, Application of He’s homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 411-418
##[11]
M. Rafei, D. D. Ganji, Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 321-328
##[12]
A. M. Siddiqui, R. Mahmood, Q. K. Ghori, Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder, Phys. Lett. A, 352 (2006), 404-410
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M. Ghasemi, M. T. Kajani, E. Babolian, Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method, Appl. Math. Comput., 188 (2007), 446-449
##[14]
J.-H. He, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Comput. Meth. Appl. Mech. Eng., 167 (1998), 69-73
##[15]
J.-H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng., 167 (1998), 57-68
##[16]
J.-H. He, Variational iteration method kind of non-linear analytical technique: some examples, Int. J. Non-Linear Mech., 34 (1999), 699-708
##[17]
J.-H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput., 114 (2000), 115-123
##[18]
S. Momani, S. Abuasad, Application of He’s variational iteration method to Helmholtz equation, Chaos Solitons Fractals, 27 (2006), 1119-1123
##[19]
A. A. Soliman, A numerical simulation and explicit solutions of KdV Burgers and Laxs seventh- order KdV equations, Chaos Solitons Fractals, 29 (2006), 294-302
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E. M. Abulwafa, M. A. Abdou, A. A. Mahmoud, The solution of nonlinear coagulation problem with mass loss, Chaos Solitons Fractals, 29 (2006), 313-330
##[21]
Z. M. Odibat, S. Momani, Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 27-36
##[22]
M. Javidi, A. Golbabai, Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method, Chaos Solitons Fractals, 36 (2008), 309-313
##[23]
I. H. Abdel-Halim Hassan, M. I. A. Othman, A. M. S. Mahdy, Variational iteration method for solving twelve order boundary value problems, Int. J. Math. Anal. (Ruse), 3 (2009), 719-730
##[24]
J.-H. He, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals, 30 (2006), 700-708
##[25]
J.-H. He, M. A. Abdou, New periodic solutions for nonlinear evolution equations using Expfunction method, Chaos Solitons Fractals, 34 (2007), 1421-1429
##[26]
J.-H. He, New interpretation of homotopy perturbation method, Internat. J. Modern Phys. B, 20 (2006), 2561-2568
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J.-H. He, Homotopy perturbation technique, Comput. Math. Appl. Mech. Eng., 178 (1999), 257-262
##[28]
J.-H. He, Homotopy perturbation method: A new nonlinear technique, Appl. Math. Comput., 135 (2003), 73-79
##[29]
J.-H. He, Periodic solutions and bifurcations of delay-differential equations, Phys. Lett. A, 347 (2005), 228-230
##[30]
J.-H. He, Homotopy-perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci. Numer. Simul., 6 (2005), 207-208
##[31]
L. Cveticanin, Homotopy-perturbation method for pure nonlinear differential equation, Chaos Solitons Fractals, 30 (2006), 1221-1230
##[32]
S. Abbasbandy, Application of He’s homotopy perturbation method for Laplace transform, Chaos Solitons Fractals, 30 (2006), 1206-1212
##[33]
A. M. Siddiqui, R. Mahmood, Q. K. Ghori, Thin film flow of athird grade fluide on a moving belt by He’s homotopy perturbation method, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 7-14
##[34]
A. M. Siddiqui, M. Ahmed, Q. K. Ghori, Couette and Poiseuille flows for non-Newtonian fluids, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 15-26
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S. J. Liao, An approximate solution technique not dependind on small parameters: A special example, Int. J. Non-Linear Mech., 30 (1995), 371-380
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J.-H. He, Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos Solitons Fractals, 19 (2004), 847-851
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H. M. Liu, Variational approach to nonlinear electrochemical system, Int. J. Nonlinear Sci. Numer. Simul., 5 (2004), 95-96
##[38]
I. H. Abdel-Halim Hassan, Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems, Chaos Solitons Fractals, 36 (2008), 53-65
##[39]
I. H. Abdel-Halim Hassan, Application to differential transformation method for solving systems of differential equations, Appl. Math. Model., 32 (2008), 2552-2559
##[40]
K. Djidjedi, E. H. Twizell, A. Boutayeb, Numerical methods for special non linear boundary value problems of order 2m., J. Comput. Appl. Math., 47 (1993), 35-45
]
On \(W_2\)- Curvature Tensor Nk-quasi Einstein Manifolds
On \(W_2\)- Curvature Tensor Nk-quasi Einstein Manifolds
en
en
We consider N(k)-quasi Einstein manifolds satisfying the conditions \(R(\xi,X). W_2 = 0,
W_2 (\xi,X).S = 0, P(\xi,X). W_2 = 0\), where \(W_2\) and \(P\) denote the \(W_2\)-curvature tensor and projective
curvature tensor, respectively.
28
32
A.
Taleshian
A. A.
Hosseinzadeh
k-nullity distribution
quasi Einstein manifold
N(k)-quasi Einstein manifold
\(W_2\)-curvature tensor
projective curvature tensor.
Article.4.pdf
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[1]
M. C. Chaki, R. K. Maity, On quasi Einstein manifolds, Publ. Math. Debrecen, 57 (2000), 297-306
##[2]
M. C. Chaki, P. K. Ghoshal, Some global properties of quasi Einstein manifolds, Publ. Math. Debrecen, 63 (2003), 635-641
##[3]
U. C. De, G. C. Ghosh, On quasi Einstein manifolds, Period. Math. Hungar., 48 (2004), 223-231
##[4]
U. C. De, G. C. Ghosh, On quasi Einstein manifolds. II, Bull. Calcutta Math. Soc., 96 (2004), 135-138
##[5]
U. C. De, G. C. Ghosh, On conformally flat special quasi Einstein manifolds, Publ. Math. Debrecen, 66 (2005), 129-136
##[6]
U. C. De, J. Sengupta, D. Saha, Conformally flat quasi-Einstein spaces, Kyungpook Math. J., 46 (2006), 417-423
##[7]
C. Özgür, N(k)-quasi Einstein manifolds satisfying certain conditions, Chaos Solitons Fractals, 38 (2008), 1373-1377
##[8]
C. Özgür, Sibel Sular, On N(k)-quasi Einstein manifolds satisfying certain conditions, Balkan J. Geom. Appl., 13 (2008), 74-79
##[9]
C. Özgür, M. M. Tripathi, On the concircular curvature tensor of an N(k)-quasi Einstein manifold, Math. Pannon., 18 (2007), 95-100
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G. P. Pokhariyal, R. S. Mishra, Curvature tensors' and their relativistics significance, Yokohoma Math. J., 18 (1970), 105-108
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S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Math. J., 40 (1988), 441-448
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M. M. Tripathi, J. S. Kim, On N(k)-quasi Einstein manifolds, Commun. Korean Math. Soc., 22 (2007), 411-417
##[13]
K. Yano, M. Kon, Structures on manifolds, World Scientic Publishing Co., Singapore (1984)
]
Complete Derivation of the Momentum Equation for the Second Grade Fluid
Complete Derivation of the Momentum Equation for the Second Grade Fluid
en
en
In a recently accepted paper of R. A. Van Gorder and K. Vajravelu [1] (Comments on "Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet") Central European Journal of Physics, DOI:10.2478/s11534-009-0145-2 (online), the authors have made momentum equation for the second grade fluid very controversial. The aim of our this communication is to give complete exact derivation of the momentum equation for second grade fluid and remedy this confusion.
33
39
Muhammad
Ayub
Haider
Zaman
Second grade fluid
Boundary layer approxmations
Thermodynamical compatibility for second grade fluid model
Article.5.pdf
[
[1]
R. A. Van Gorder, K. Vajravelu, Comment on “Series solution of hydromagnetic flow and heat transfer with hall effect in a second grade fluid over a stretching sheet”, Centr. Eur. J. Phys., 8 (2010), 514-515
##[2]
S. K. Khan, E. Sanjayanand, Viscoelastic boundary layer MHD flow through a porous medium over a porous quadratic stretching sheet, Archives of Mechanics, 56 (2004), 191-204
##[3]
S. Abdel, P. H. Veena, K. Rajgopal, V. K. Parvin, Non-Newtonian magnetohydrodynamic flow over a stretching surface with heat and mass transfer, Int. J. Non-Linear Mech., 39 (2004), 1067-1078
##[4]
M. S. Abdel, M. M. Nandeppanavar, Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with non-uniform heat source/sink, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 2120-2131
##[5]
J. E. Dunn, K. R. Rajagopal, Fluids of differential type: Critical review and thermodynamic analysis, Int. J. Eng. Sci., 33 (1995), 689-729
##[6]
H. Zaman, M. Ayub, Reply to the comments on: ”Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet”, Centr. Eur. J. Phys., 8 (2010), 516-518
##[7]
K. Vajravelu, D. Rollins, Hydromagnetic flow of a second grade fluid over a stretching sheet, Appl. Math. Comput., 148 (2004), 783-791
##[8]
M. Sajid, T. Hayat, S. Asghar, Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet, Int. J. Heat Mass Transfer, 50 (2007), 1723-1736
##[9]
T. Hayat, Z. Abbas, I. Pop, Momentum and heat transfer over a continuously moving surface with a parallel free stream in a viscoelastic fluid, Numer. Methods Partial Differential Equations, 26 (2010), 305-319
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F. M. Hady, R. S. R Gorla, Heat transfer from a continuous surface in a parallel free stream of viscoelastic fluid, Acta Mechanica, 128 (1998), 201-208
##[11]
K. Sadeghy, M. Sharifi, Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate, Int. J. Non-linear Mech., 39 (2004), 1265-1273
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R. S. Rivilin, J. L. Ericksen, Stress-Deformation Relations for Isotropic Materials, J. Rational Mech. Anal., 4 (1955), 323-425
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R. L. Fosdick, K. R. Rajagopal, Anomalous features in the model of “second order fluids”, Arch. Rational Mech. Anal., 70 (1979), 145-152
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J. E. Dunn, R. L. Fosdick, Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade, Arch. Rational Mech. Anal., 56 (1974), 191-252
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H. Schlichting, K. Gersten, Boundary-layer theory, Springer-Verlag, Berlin (2000)
]
A £-fuzzy Fixed Point Theorem in Partially Ordered Sets and Applications
A £-fuzzy Fixed Point Theorem in Partially Ordered Sets and Applications
en
en
An analogue of £-fuzzy Banach's fixed point theorem in partially ordered sets is proved in this paper, and
several applications to linear and nonlinear matrix equations are discussed.
40
45
H.
Eshaghi-Kenari
£-Fuzzy contractive mapping
Complete £-fuzzy metric space
Fixed point theorem
Article.6.pdf
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[1]
A. Bjorner, Order-reversing maps and unique fixed points in complete lattices, Algebra Universalis, 12 (1981), 402-403
##[2]
G. Deschrijver, C. Cornelis, E. E. Kerre, On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Trans. Fuzzy Syst., 12 (2004), 45-61
##[3]
G. Deschrijver, E. E. Kerre, On the relationship between some extensions of fuzzy Set theory, Fuzzy Sets and Systems, 133 (2003), 227-235
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##[7]
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039-1046
##[8]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443
##[9]
R. Saadati, A. Razani, H. Adibi, A Common fixed point theorem in L-fuzzy metric spaces, Chaos Solitons Fractals, 33 (2007), 358-363
##[10]
R. Saadati, J. H. Park, On the Intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27 (2006), 331-344
##[11]
R. Saadati, J. H. Park, Intuitionistic fuzzy Euclidean normed spaces, Commun. Math. Anal., 1 (2006), 85-90
]
Solution of Systems of Integral-Differential Equations by Variational Iteration Method
Solution of Systems of Integral-Differential Equations by Variational Iteration Method
en
en
In this paper, we will consider variational iteration method (VIM) for solving
systems of integral–differential equation. This method is based on the use of
Lagrange multipliers for identification of optimal value of a parameter in a
functional. Using the variational iteration method, it is possible to find the
exact solution or an approximate solution of the problem. In this paper,
variational iteration method is introduced to overcome the difficulty arising in
calculating Adomian polynomials.
46
57
M.
Matinfar
M.
Ghanbari
Variational iteration method
Systems of integral–differential equations.
Article.7.pdf
[
[1]
M. A. Abdou , A. A. Soliman, Variational iteration method for solving Burger’s and coupled Burger’s equation, J. Comput. Appl. Math., 181 (2005), 245-251
##[2]
J. Biazar, Solution of system of integral–differential equations by Adomian decomposition method, Appl. Math. Comput., 168 (2005), 1232-1238
##[3]
N. Bildik, A. Konuralp, The use of variational iteration method, differential transform method and Adomian decomposition method for solving different type of nonlinear partial differential equations, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 65-70
##[4]
J.-H. He, X.-H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Choas Solitons Fractals, 29 (2006), 108-113
##[5]
J.-H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, Int. J. Non-Linear Mech., 34 (1999), 699-708
##[6]
J.-H. He, Variational iteration method for autonomous ordinary differential system, Appl. Math. Comput., 114 (2000), 115-123
##[7]
J.-H. He, Approximate solution of nonlinear differential equations with convolution product non-linearities, Comput. Methods Appl. Mech. Engrg., 167 (1998), 69-73
##[8]
J.-H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engrg., 167 (1998), 57-68
##[9]
J.-H. He, Variational theoryfor linear magneto-electero-elasticity, Int. J. Nonlinear Sci. Numer. Simul., 2 (2001), 309-316
##[10]
M. Inokuti, H. Sekine, T. Mura, General use of the Lagrange multiplier in nonlinear mathematical physics, Variationalmethod in the Mechanics of solids, pergamon press, 1978 (1978), 62-156
##[11]
S. Momani, S. Abuasad, Application of He’s variational iteration method to Helmholtz equation, Chaos Solitons Fractals, 27 (2006), 1119-1123
##[12]
Z. M. Odibat, S. Momani, Application of variational method to nonlinear differential equations of fractional order, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 27-36
##[13]
A. A. Soliman, Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method, Math. Comput. Simulation, 70 (2005), 119-124
]