Approximate analytical solution for seepage flow with fractional derivatives in porous media

Keywords

Linearization, Porous medium, Darcy's law, Nonlinear system, Mathematics

References

• The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transferBruce A. Finlayson — 1972
• A new approach to nonlinear partial differential equationsJi‐Huan He — 1997
• Existence and Uniqueness for a Nonlinear Fractional Differential EquationDomenico Delbosco, Luigi Rodino — 1996
• A review of the decomposition method in applied mathematicsG. Adomian — 1988
• Variational iteration method for delay differential equationsJi‐Huan He — 1997
• ON THE SOLUTION OF SOME SIMPLE FRACTIONAL DIFFERENTIAL EQUATIONSL. M. B. C. Campos — 1990
• General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics1M. Inokuti, H. Sekine, T. Mura — 1980

Cited by

• Application of Homotopy-Perturbation Method for Solving Gas Dynamics EquationHossein Jafari, Mehdi Zabihi, Mohammad Saidy — 2008
• Theory, Methods, and Applications of Fractional CalculusK. Mohat, B. L. Choudhary — 2014
• Preface: Variational iteration method-Reality, potential, and challengesLan Xu, Ji‐Huan He, Abdul–Majid Wazwaz — 2007
• Fractional radial diffusion equation analytical solution via Hankel and Sumudu transformsV. B. L. Chaurasia, Ravi Shanker Dubey, Fethi Bin Muhammad Belgacem — 2012
• A step variational iteration method for solving non-chaotic and chaotic systemsR. Yulita Molliq, Mohd Salmi Md Noorani, Rokiah Rozita Ahmad — 2013
• A Modified Perturbation Technique Depending Upon an Artificial ParameterJi‐Huan He — 2000
• Analysis of A Fractional-Order Competition Model with Common Inhibitory EffectSwarnali Sharma, G. P. Samanta — 2013
• Solution of Seventh Order Boundary Value Problems by Variational Iteration TechniqueShahid S. Siddiqi, Ghazala Akram, Muzammal Iftikhar — 2012
• On the numerical solution of linear stiff IVPs by modified homotopy perturbation methodMd. Sazzad Hossien Chowdhury, Ishak Hashim, Md. Mahmudur Rahman — 2011
• On the application of partial differential equations and fractional partial differential equations to images and their methods of solutionByron A. Jacobs — 2014
• New Approach to Find the Exact Solution of Fractional Partial Differential EquationAbdolamir Karbalaie, Mohammad Mehdi Montazeri, Hamed Hamid Muhammed — 2012
• APPLICATION OF HOMOTOPY ANALYSIS TRANSFORM METHOD TO FRACTIONAL BIOLOGICAL POPULATION MODELHabibolla Latifizadeh — 2013
• Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equationS. Abbasbandy, Saeed Kazem, Mohammed S. Alhuthali — 2015
• Applications of the variational iteration method to fractional diffusion equations: local versus nonlocal onesGuo–Cheng Wu — 2012
• Generalized Continuous Time Random Walks, Master Equations, and Fractional Fokker-Planck EquationsChristopher N. Angstmann, I. C. Donnelly, B. I. Henry — 2015
• Numerical Solution of Space-Time Fractional Convection-Diffusion Equations with Variable Coefficients Using Haar WaveletsJinxia Wei, Yiming Chen, Baofeng Li — 2012
• THE EXACT SOLUTION OF DELAY DIFFERENTIAL EQUATIONS USING COUPLING VARIATIONAL ITERATION WITH TAYLOR SERIES AND SMALL TERMYulita Molliq Rangkuti, Mohd Salmi Md Noorani — 2012
• Peristaltic Transport of a Nanofluid in an Inclined TubeK. Maruthi Prasad, N. Subadra, M. A. S. Srinivas — 2015
• Variational Iteration Method for Solving Systems of Linear Delay Differential EquationsSara Barati, Karim Ivaz — 2012
• Time-fractional effect on pressure waves propagating through a fluid filled circular long elastic tubeEssam M. Abulwafa, Ε. K. El-Shewy, Abeer A. Mahmoud — 2016

Related papers

• Linearization of seismic response of structures equipped with nonlinear viscous dampers using perturbation techniqueAfshin Moslehi Tabar — 2019
• Primary study of permeability of porous mediaXinhua Xue — 2009
• The simulation of the flow through the porous media and diffusible barriersMartin Kynčl, Jaroslav Pelant — 2018
• Simulations of Single-Fluid Flow in Porous MediaAntti Koponen, Markku Kataja, J. Timonen — 1998
• A new analytical method for solving nonlinear biological population modelSafaa Hamid Mahdi, Hassan Kamil Jassim, Nabeel Jawad Hassan — 2022
• A coupling concept for two‐phase compositional porous‐medium and single‐phase compositional free flowKlaus Mosthaf, K. Baber, Bernd Flemisch — 2011
• Research on unsteady well flow of the specific discharge of the nonlinear regimeChang An-ding — 2005
• A model of solute diffusion in unsaturated double-porosity medium by homogenizationDung Ngoc Tien Tran, Quang Minh Pham, Thong Nguyen — 2018