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

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DOI10.1016/S0045-7825(98)00108-XzbMath0942.76077WikidataQ127012652 ScholiaQ127012652MaRDI QIDQ1808067

Publication date: 30 November 1999

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

fractional derivatives approximate solutions porous media Darcy law variational iteration method seepage flow

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Variational methods applied to problems in fluid mechanics (76M30)

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method for non-smooth initial value problems, Solving a fractional order model of HIV infection of \(CD4^{+}\) T cells, Numerical simulation of fractional Fornberg-Whitham equation by differential transformation method, The HPM applied to MHD nanofluid flow over a horizontal stretching plate, Fractional variational iteration method and its application, Approximate rational Jacobi elliptic function solutions of the fractional differential equations via the enhanced Adomian decomposition method, Numerical solution of two-sided space-fractional wave equation using finite difference method, Modeling of nonlinear boundary value problems in enzyme-catalyzed reaction diffusion processes, On Legendre polynomial approximation with the VIM or HAM for numerical treatment of nonlinear fractional differential equations, Local and global existence of mild solutions for impulsive fractional semilinear integro-differential equation, Analytic solutions for generalized forms of the nonlinear heat conduction equation, Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations, Analytical methods for solving the time-fractional Swift-Hohenberg (S-H) equation, He's variational iteration method applied to the solution of the prey and predator problem with variable coefficients, Construction of solitary solutions for nonlinear dispersive equations by variational iteration method, Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach-Adomian-meyers modified decomposition method, Solution of wave equation in radial form by VIM, Some results for fractional impulsive boundary value problems on infinite intervals, Axisymmetric solutions to time-fractional heat conduction equation in a half-space under Robin boundary conditions, Variational iteration method for solving the multi -- pantograph delay equation, Existence of solutions for nonlinear impulsive fractional differential equations of order \(\alpha \in (2, 3\) with nonlocal boundary conditions], Numerical simulation of the FitzHugh-Nagumo equations, A new fractional analytical approach via a modified Riemann-Liouville derivative, Variational iteration method for the time-fractional Fornberg-Whitham equation, The effective thermal conductivity of porous media based on statistical self-similarity, On approximate solutions for fractional logistic differential equation, On the numerical solution of the model for HIV infection of \(CD4^{+}\) T cells, On fractional integro-differential equations with state-dependent delay, A new application of the homotopy analysis method in solving the fractional Volterra's population system., Numerical computation of nonlinear fractional Zakharov-Kuznetsov equation arising in ion-acoustic waves, An efficient method for solving Emden-Fowler equations, Comment on ``An approximation to solution of space and time fractional telegraph equations by He's variational iteration method, Fractional variational iteration method for fractional initial-boundary value problems arising in the application of nonlinear science, A tutorial review on fractal spacetime and fractional calculus, Numerical comparison of methods for solving fractional differential-algebraic equations (FDAEs), Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation, A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations, A short remark on fractional variational iteration method, Analysis of projectile motion in view of fractional calculus, Homotopy perturbation method for fractional Fornberg-Whitham equation, Existence of solutions to fractional mixed integrodifferential equations with nonlocal initial condition, An analytic algorithm for the space-time fractional advection-dispersion equation, Modified step variational iteration method for solving fractional biochemical reaction model, Application of He's variational iteration method in nonlinear boundary value problems in enzyme-substrate reaction diffusion processes. I: The steady-state amperometric response, Solving systems of fractional differential equations by homotopy-perturbation method, Adaptation of homotopy-perturbation method for numeric-analytic solution of system of ODEs, Application of He's variational iteration method to nonlinear heat transfer equations, Compact and noncompact structures for nonlinear fractional evolution equations, Analytical solutions to heat transfer equations by homotopy-perturbation method revisited, Variational iteration method for solving Burgers and coupled Burgers equations, An efficient analytical approach for solving fourth order boundary value problems, A spectral domain decomposition approach for the generalized Burger's-Fisher equation, An efficient technique for finding the eigenvalues of fourth-order Sturm-Liouville problems, A new domain decomposition algorithm for generalized Burgers-Huxley equation based on Chebyshev polynomials and preconditioning, Numerical and explicit solutions of the fifth-order Korteweg-de Vries equations, Variational iteration method for solving integro-differential equations, The variational iteration method for solitary patterns solutions of gBBM equation, Application of homotopy-perturbation method to nonlinear population dynamics models, Relative controllability of linear systems of fractional order with delay, Some existence results on boundary value problems for fractional \(p\)-Laplacian equation at resonance, ANALYTICAL APPROACHES FOR SYSTEM OF NONLINEAR EQUATIONS ARISING IN MELTING OF A FINITE SLAB, APPLICATION OF He's VARIATIONAL ITERATION METHOD AND ADOMIAN'S DECOMPOSITION METHOD TO PROCHHAMMER–CHREE EQUATION, Unnamed Item, Hilfer fractional differential equations with almost sectorial operators, Subordination principle and approximation of fractional resolvents and applications to fractional evolution equations, Approximate solutions to fractional differential equations, MODIFICATION OF OPTIMAL HOMOTOPY ASYMPTOTIC METHOD FOR MULTI-DIMENSIONAL TIME-FRACTIONAL MODEL OF NAVIER–STOKES EQUATION, NUMERICAL ANALYSIS OF FRACTIONAL-ORDER EMDEN–FOWLER EQUATIONS USING MODIFIED VARIATIONAL ITERATION METHOD, Unnamed Item, Modified Differential Transform Method for Solving Black-Scholes Pricing Model of European Option Valuation Paying Continuous Dividends, Numerical solution of reaction-diffusion equations with convergence analysis, Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative, Two-dimensional nonlinear time fractional reaction-diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media, Dark and kink soliton solutions of the generalized ZK-BBM equation by iterative scheme, A New Compact Numerical Scheme for Solving Time Fractional Mobile-Immobile Advection-Dispersion Model, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, A Novel Method to Improve the Multiple-Scales Solution of the Forced Nonlinear Oscillators, Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials, Variational iteration method for autonomous ordinary differential systems, Approximate analytical solution of Blasius' equation, Application of He's homotopy perturbation and He's variational iteration methods for solution of Benney–Lin equation, A new analytical approximate method for the solution of fractional differential equations, Fractional Variational Iteration Method for Time Fractional Fourth-Order Diffusion-Wave Equation, SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS, Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media, An accurate numerical method for solving the generalized time-fractional diffusion equation, Approximate analytical solution of Blasius' equation, Analytical solution for a suspension bridge by applying HPM and VIM, Numerical solution of fractional differential equations using fractional Chebyshev polynomials, Generalized Continuous Time Random Walks, Master Equations, and Fractional Fokker--Planck Equations, CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel, Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

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