A Tutorial Review on Fractal Spacetime and Fractional Calculus

[1]  Stuart Macdonald,et al.  Emperor’s New Clothes , 2015 .

[2]  M. Matinfar,et al.  Application of variational iteration method to nonlinear heat transfer equations using He's polynomials , 2013 .

[3]  M. E. Naschie,et al.  The quantum gravity Immirzi parameter—A general physical and topological interpretation , 2013 .

[4]  Fujuan Liu,et al.  Silk Cocoon: "Emperor's New Clothes" for Pupa: Fractal Nano-Hydrodynamical Approach , 2013 .

[5]  Ji-Huan He,et al.  Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology , 2013 .

[6]  M. Naschie A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory , 2013 .

[7]  M. Naschie A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light , 2013 .

[8]  Ji-Huan He,et al.  Exp-function Method for Fractional Differential Equations , 2013, International Journal of Nonlinear Sciences and Numerical Simulation.

[9]  Ai-Min Yang,et al.  THE YANG-FOURIER TRANSFORMS TO HEAT-CONDUCTION IN A SEMI-INFINITE FRACTAL BAR , 2013 .

[10]  Li-Mei Yan MODIFIED HOMOTOPY PERTURBATION METHOD COUPLED WITH LAPLACE TRANSFORM FOR FRACTIONAL HEAT TRANSFER AND POROUS MEDIA EQUATIONS , 2013 .

[11]  Jie Fan,et al.  FRACTAL HEAT TRANSFER IN WOOL FIBER HIERARCHY , 2013 .

[12]  G. Wu,et al.  VARIATIONAL ITERATION METHOD FOR THE q -DIFFUSION EQUATIONS ON TIME SCALES , 2013 .

[13]  Jie Fan,et al.  WATER PERMEATION IN THE BRANCHING CHANNEL NET OF WOOL FIBER , 2013 .

[14]  Ji-Huan He,et al.  Local Fractional Variational Iteration Method for Fractal Heat transfer in Silk Cocoon hierarchy , 2013 .

[15]  Xiao‐Jun Yang,et al.  Fractal heat conduction problem solved by local fractional variation iteration method , 2013 .

[16]  Chun-Feng Liu,et al.  Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem , 2013 .

[17]  Ji-Huan He Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials” , 2012 .

[18]  Ji-Huan He,et al.  Asymptotic Methods for Solitary Solutions and Compactons , 2012 .

[19]  Jihuan He,et al.  Fractal Derivative Model for Air Permeability in Hierarchic Porous Media , 2012 .

[20]  S. Mohyud-Din,et al.  Modified variational iteration method for solving a neutral functional‐differential equation with proportional delays , 2012 .

[21]  Atulya K. Nagar,et al.  He-Laplace Method for Linear and Nonlinear Partial Differential Equations , 2012, J. Appl. Math..

[22]  K. N. Rai,et al.  Application of He's homotopy perturbation method for multi‐dimensional fractional Helmholtz equation , 2012 .

[23]  S. M. Hosseini,et al.  Variational iteration method for Hirota‐Satsuma coupled KdV equation using auxiliary parameter , 2012 .

[24]  Yanqin Liu Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method , 2012 .

[25]  Najeeb Alam Khan,et al.  Numerical solutions of time‐fractional Burgers equations: A comparison between generalized differential transformation technique and homotopy perturbation method , 2012 .

[26]  Hsuan-Ku Liu,et al.  Application of the Variational Iteration Method to Strongly Nonlinear q-Difference Equations , 2012, J. Appl. Math..

[27]  Ji-Huan He,et al.  Homotopy Perturbation Method with an Auxiliary Term , 2012 .

[28]  Ji-Huan He,et al.  Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus , 2012 .

[29]  Ji-Huan He,et al.  Exact solutions of time-fractional heat conduction equation by the fractional complex transform , 2012 .

[30]  Ji-Huan He,et al.  Fractional model for heat conduction in polar bear hairs , 2012 .

[31]  Habibolla Latifizadeh Application of Homotopy Perturbation and Numerical Methods to the Circular Porous Slider , 2012 .

[32]  Ji-Huan He,et al.  BIOMIMIC DESIGN OF MULTI-SCALE FABRIC WITH EFFICIENT HEAT TRANSFER PROPERTY , 2012 .

[33]  Ji-Huan He,et al.  THE FRACTAL HARMONIC LAW AND ITS APPLICATION TO SWIMMING SUIT , 2012 .

[34]  Hai-Yan Kong,et al.  A novel friction law , 2012 .

[35]  Ji-Huan He,et al.  Review on fiber morphology obtained by bubble electrospinning and blown bubble spinning , 2012 .

[36]  J. He The Smaller, the Better: From the Spider-Spinning to Bubble-Electrospinning , 2012 .

[37]  Wu Guo-Cheng,et al.  Variational Iteration Method for q-Difference Equations of Second Order , 2012, J. Appl. Math..

[38]  G. Wu,et al.  LAPLACE TRANSFORM OVERCOMING PRINCIPLE DRAWBACKS IN APPLICATION OF THE VARIATIONAL ITERATION METHOD TO FRACTIONAL HEAT EQUATIONS , 2012 .

[39]  Ji-Huan He,et al.  A SHORT REMARK ON FRACTIONAL VARIATIONAL ITERATION METHOD , 2011 .

[40]  Yasir Khan,et al.  On the coupling of the homotopy perturbation method and Laplace transformation , 2011, Math. Comput. Model..

[41]  Hongqing Zhang,et al.  An Exp-function method for new N-soliton solutions with arbitrary functions of a (2+1)-dimensional vcBK system , 2011, Comput. Math. Appl..

[42]  Yasir Khan,et al.  Homotopy perturbation transform method for nonlinear equations using He's polynomials , 2011, Comput. Math. Appl..

[43]  E. Haven Itô’s Lemma with Quantum Calculus (q-Calculus): Some Implications , 2011 .

[44]  N. Samec,et al.  Numerical optimization of a waste-to-energy plant's operating parameters using CFD , 2011 .

[45]  Ji-Huan He A NEW FRACTAL DERIVATION , 2011 .

[46]  Ji-Huan He,et al.  Fractional Complex Transform for Fractional Differential Equations , 2010 .

[47]  Xumei Chen,et al.  The variational iteration method for solving a neutral functional-differential equation with proportional delays , 2010, Comput. Math. Appl..

[48]  Ji-Huan He,et al.  A NOTE ON THE HOMOTOPY PERTURBATION METHOD , 2010 .

[49]  Wen Chen,et al.  Investigation on Fractional and Fractal Derivative Relaxation- Oscillation Models , 2010 .

[50]  Majid Khan,et al.  Homotopy Perturbation Method for Nonlinear Exponential Boundary Layer Equation using Laplace Transformation, He's Polynomials and Pade Technology He's Polynomials and Pade Technology , 2010 .

[51]  S. Zhang,et al.  A GENERALIZED EXP-FUNCTION METHOD FOR FRACTIONAL RICCATI DIFFERENTIAL EQUATIONS , 2010 .

[52]  Ji-Huan He Frontier of Modern Textile Engineering and Short Remarks on Some Topics in Physics , 2010 .

[53]  K. Noor,et al.  On the Coupling of He's Polynomials and Laplace Transformation , 2010 .

[54]  Habibolla Latifizadeh Coupling of He's polynomials and Laplace transformation for MHD viscous flow over a stretching sheet , 2010 .

[55]  F. Austin,et al.  THE VARIATIONAL ITERATION METHOD WHICH SHOULD BE FOLLOWED , 2010 .

[56]  Ji-Huan He Hilbert cube model for fractal spacetime , 2009 .

[57]  M. E. Naschie Deriving the curvature of fractal-Cantorian spacetime from first principles , 2009 .

[58]  Guy Jumarie,et al.  From Lagrangian mechanics fractal in space to space fractal Schrödinger’s equation via fractional Taylor’s series , 2009 .

[59]  Arash Gholami Davoodi,et al.  Solutions for the double Sine‐Gordon equation by Exp‐function, Tanh, and extended Tanh methods , 2009 .

[60]  Ji-Huan He A generalized poincaré-invariant action with possible application in strings and E-infinity theory , 2009 .

[61]  Asghar Ghorbani,et al.  Beyond Adomian polynomials: He polynomials , 2009 .

[62]  Ahmet Yildirim,et al.  An Algorithm for Solving the Fractional Nonlinear Schrödinger Equation by Means of the Homotopy Perturbation Method , 2009 .

[63]  Z. Dai,et al.  Double Exp-function Method and Application , 2009 .

[64]  G. Wu,et al.  Fractal Approach to Flow through Porous Material , 2009 .

[65]  Ji-Huan He AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING , 2008 .

[66]  M. E. Naschie Kaluza-Klein unification - Some possible extensions , 2008 .

[67]  Hossein Jafari,et al.  Application of the homotopy perturbation method to coupled system of partial differential equations with time fractional derivatives , 2008 .

[68]  Shaher Momani,et al.  Applications of variational iteration and homotopy perturbation methods to fractional evolution equations , 2008 .

[69]  Qi Wang Homotopy perturbation method for fractional KdV-Burgers equation , 2008 .

[70]  Y. Liu,et al.  A HIERARCHY OF MOTION IN ELECTROSPINNING PROCESS AND Ε-INFINITY NANOTECHNOLOGY , 2008 .

[71]  M. Noor,et al.  Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials , 2008 .

[72]  Subir Das,et al.  Solution of Fractional Vibration Equation by the Variational Iteration Method and Modified Decomposition Method , 2008 .

[73]  Ji-Huan He A New Resistance Formulation for Carbon Nanotubes , 2008 .

[74]  Hossein Jafari,et al.  SOLVING FRACTIONAL DIFFUSION AND WAVE EQUATIONS BY MODIFIED HOMOTOPY PERTURBATION METHOD , 2007 .

[75]  Ji-Huan He Variational iteration method—Some recent results and new interpretations , 2007 .

[76]  Ji-Huan He,et al.  Variational iteration method: New development and applications , 2007, Comput. Math. Appl..

[77]  Shaher Momani,et al.  Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations , 2007, Comput. Math. Appl..

[78]  Ji-Huan He,et al.  Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method , 2007, Comput. Math. Appl..

[79]  Shaher Momani,et al.  Homotopy perturbation method for nonlinear partial differential equations of fractional order , 2007 .

[80]  Guy Jumarie,et al.  Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution , 2007 .

[81]  Asghar Ghorbani,et al.  He's Homotopy Perturbation Method for Calculating Adomian Polynomials , 2007 .

[82]  Guy Jumarie,et al.  The Minkowski's space-time is consistent with differential geometry of fractional order , 2007 .

[83]  N. Quirke,et al.  Fluid flow in carbon nanotubes and nanopipes. , 2007, Nature nanotechnology.

[84]  G. Hummer Water, proton, and ion transport: from nanotubes to proteins , 2007 .

[85]  Ahmet Boz,et al.  Exact Solutions for a Class of Nonlinear Partial Differential Equations using Exp-Function Method , 2007 .

[86]  Prince Abdullah bin Ghazi,et al.  Modified homotopy perturbation method : Application to quadratic Riccati differential equation of fractional order , 2007 .

[87]  M. E. Naschie,et al.  Elementary prerequisites for E-infinity . (Recommended background readings in nonlinear dynamics, geometry and topology) , 2006 .

[88]  M. E. Naschie,et al.  Nanotechnology for the developing world , 2006 .

[89]  Ji-Huan He,et al.  Exp-function method for nonlinear wave equations , 2006 .

[90]  G. Drăgănescu,et al.  Application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives , 2006 .

[91]  G. Jumarie,et al.  Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results , 2006, Comput. Math. Appl..

[92]  Ji-Huan He SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[93]  W. Chen Time-space fabric underlying anomalous diffusion , 2005, math-ph/0505023.

[94]  S. Momani,et al.  Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .

[95]  Necdet Bildik,et al.  The Use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations , 2006 .

[96]  Mainak Majumder,et al.  Nanoscale hydrodynamics: Enhanced flow in carbon nanotubes , 2005, Nature.

[97]  M. E. Naschie,et al.  A review of E infinity theory and the mass spectrum of high energy particle physics , 2004 .

[98]  M. E. Naschie,et al.  The VAK of vacuum fluctuation,: Spontaneous self-organization and complexity theory interpretation of high energy particle physics and the mass spectrum , 2003 .

[99]  Nabil T. Shawagfeh,et al.  Analytical approximate solutions for nonlinear fractional differential equations , 2002, Appl. Math. Comput..

[100]  M. E. Naschie,et al.  Quantum loops, wild topology and fat Cantor sets in transfinite high-energy physics , 2002 .

[101]  Ji-Huan He A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[102]  Ji-Huan He Homotopy perturbation technique , 1999 .

[103]  G. Ord Fractals and the Quantum Classical Boundary , 1999 .

[104]  Ji-Huan He Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[105]  Ji-Huan He Approximate analytical solution for seepage flow with fractional derivatives in porous media , 1998 .

[106]  G. Ord Fractal space-time and the statistical mechanics of random walks , 1996 .

[107]  D. Finkelstein Quantum sets and clifford algebras , 1982 .