Numerical Computation of a Fractional Model of Differential-Difference Equation

[1]  D. Ganji,et al.  Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model , 2015 .

[2]  S. A. Moshizi,et al.  An analytical study on unsteady motion of vertically falling spherical particles in quiescent power-law shear-thinning fluids , 2014 .

[3]  J. H. He,et al.  Differential-difference model for nanotechnology , 2008 .

[4]  Ji-Huan He,et al.  Nano-effects, quantum-like properties in electrospun nanofibers , 2007 .

[5]  Devendra Kumar,et al.  Numerical study for time-fractional Schrödinger equations arising in quantum mechanics , 2014 .

[6]  J. A. Tenreiro Machado,et al.  New Trends in Nanotechnology and Fractional Calculus Applications , 2010 .

[7]  Shyam L. Kalla,et al.  ANALYTICAL INVESTIGATIONS OF THE SUMUDU TRANSFORM AND APPLICATIONS TO INTEGRAL PRODUCTION EQUATIONS , 2003 .

[8]  S D Zhu,et al.  Exp-function Method for the Discrete mKdV Lattice , 2007 .

[9]  E. Babolian,et al.  An efficient method for nonlinear fractional differential equations: combination of the Adomian decomposition method and spectral method , 2014 .

[10]  Satish Nagarajaiah,et al.  An analytical method for analyzing symmetry-breaking bifurcation and period-doubling bifurcation , 2015, Commun. Nonlinear Sci. Numer. Simul..

[11]  Davood Domiri Ganji,et al.  Heat transfer of Cu-water nanofluid flow between parallel plates , 2013 .

[12]  Mohammad Mehdi Rashidi,et al.  Steady nanofluid flow between parallel plates considering thermophoresis and Brownian effects , 2016 .

[13]  Shijun Liao,et al.  Homotopy Analysis Method in Nonlinear Differential Equations , 2012 .

[14]  I. Podlubny Fractional differential equations , 1998 .

[15]  V. E. Tarasov Three-dimensional lattice models with long-range interactions of Grünwald–Letnikov type for fractional generalization of gradient elasticity , 2016 .

[16]  Davood Domiri Ganji,et al.  Investigation of the heat transfer of a non-Newtonian fluid flow in an axisymmetric channel with porous wall using Parameterized Perturbation Method (PPM) , 2014, J. Frankl. Inst..

[17]  Suheil A. Khuri,et al.  A Laplace decomposition algorithm applied to a class of nonlinear differential equations , 2001 .

[18]  J. Machado,et al.  Analytical Solution of Fractional Order Diffusivity Equation With Wellbore Storage and Skin Effects , 2016 .

[19]  Yu-Ming Chu,et al.  The homotopy perturbation method for discontinued problems arising in nanotechnology , 2009, Comput. Math. Appl..

[20]  Ji-Huan He,et al.  Bubble Electrospinning for Mass Production of Nanofibers , 2007 .

[21]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[22]  A. Wazwaz,et al.  Solving New Fourth–Order Emden–Fowler-Type Equations by the Adomian Decomposition Method , 2015 .

[23]  Davood Domiri Ganji,et al.  Entropy generation of nanofluid in presence of magnetic field using Lattice Boltzmann Method , 2015 .

[24]  Abdul-Majid Wazwaz,et al.  A reliable algorithm for positive solutions of nonlinear boundary value problems by the multistage Adomian decomposition method , 2014 .

[25]  Davood Domiri Ganji,et al.  Investigation of squeezing unsteady nanofluid flow using ADM , 2013 .

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

[27]  Mohammad Mehdi Rashidi,et al.  Predictor homotopy analysis method for nanofluid flow through expanding or contracting gaps with permeable walls , 2015 .

[28]  Devendra Kumar,et al.  Analytical modeling for fractional multi-dimensional diffusion equations by using Laplace transform , 2015 .

[29]  Vidhya Saraswathy Krishnasamy,et al.  The Numerical Solution of the Bagley–Torvik Equation With Fractional Taylor Method , 2016 .

[30]  Zaid Odibat,et al.  An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials , 2015 .

[31]  R. Magin Fractional Calculus in Bioengineering , 2006 .

[32]  Devendra Kumar,et al.  Numerical computation of fractional Black–Scholes equation arising in financial market , 2014 .

[33]  Davood Domiri Ganji,et al.  Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM , 2015 .

[34]  Devendra Kumar,et al.  Numerical study for systems of fractional differential equations via Laplace transform , 2015 .

[35]  Yong Liu,et al.  Micro sphere with nanoporosity by electrospinning , 2007 .

[36]  Dominik Sierociuk,et al.  Diffusion process modeling by using fractional-order models , 2015, Appl. Math. Comput..

[37]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[38]  Devendra Kumar,et al.  Homotopy Analysis Sumudu Transform Method for Nonlinear Equations , 2012 .

[39]  Kunjan Shah,et al.  The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology , 2015 .

[40]  G. K. Watugala,et al.  Sumudu Transform - a New Integral Transform to Solve Differential Equations and Control Engineering Problems , 1992 .

[41]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[42]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[43]  T. Hayat,et al.  MHD free convection of Al2O3–water nanofluid considering thermal radiation: A numerical study , 2016 .

[44]  Adem Kilicman,et al.  Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations , 2014 .

[45]  Devendra Kumar,et al.  Numerical computation of fractional Lotka-Volterra equation arising in biological systems , 2015 .

[46]  Fethi Bin Muhammad Belgacem,et al.  Extraction of the Laplace, Fourier, and Mellin transforms from the Sumudu transform , 2014 .

[47]  H. Ouakad,et al.  Analytical Solution for the Forced Vibrations of a Nano-Resonator with Cubic Nonlinearities Using Homotopy Analysis Method , 2015 .

[48]  Hari M. Srivastava,et al.  Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets , 2014 .

[49]  Devendra Kumar,et al.  A reliable algorithm for solving discontinued problems arising in nanotechnology , 2013 .

[50]  S. Liao An approximate solution technique not depending on small parameters: A special example , 1995 .

[51]  Francesco Mainardi,et al.  Fractional relaxation with time-varying coefficient , 2014 .

[52]  A. M. Mathai,et al.  Fractional Reaction-Diffusion Equations , 2006, math/0604473.

[53]  Davood Domiri Ganji,et al.  Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls , 2015 .

[54]  G. Maione,et al.  Reduced fractional modeling of 3D video streams: the FERMA approach , 2015 .

[55]  Mohammad Mehdi Rashidi,et al.  Effect of space dependent magnetic field on free convection of Fe3O4–water nanofluid , 2015 .

[56]  Mohammad Mehdi Rashidi,et al.  Effect of non-uniform magnetic field on forced convection heat transfer of Fe3O4–water nanofluid , 2015 .