Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation

From MaRDI portal
Publication:747993

DOI10.1007/s11071-014-1854-7zbMath1345.65060OpenAlexW1969399740MaRDI QIDQ747993

Ali H. Bhrawy, Mahmoud A. Zaky

Publication date: 19 October 2015

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-014-1854-7




Related Items (only showing first 100 items - show all)

The construction of a new operational matrix of the distributed-order fractional derivative using Chebyshev polynomials and its applicationsNew numerical algorithm to solve variable-order fractional integrodifferential equations in the sense of Hilfer-Prabhakar derivativeNon-local telegrapher's equation as a transmission line modelA numerical scheme based on the Chebyshev functions to find approximate solutions of the coupled nonlinear sine-Gordon equations with fractional variable ordersInvariant solutions of fractional-order spatio-temporal partial differential equationsAn easy to implement linearized numerical scheme for fractional reaction-diffusion equations with a prehistorical nonlinear source functionThe direct meshless local Petrov-Galerkin technique with its error estimate for distributed-order time fractional cable equationTHE NUMERICAL MESHLESS APPROACH FOR SOLVING THE 2D TIME NONLINEAR MULTI-TERM FRACTIONAL CABLE EQUATION IN COMPLEX GEOMETRIESA Chebyshev collocation method for solving the non-linear variable-order fractional Bagley-Torvik differential equationFinite difference/collocation method to solve multi term variable‐order fractional reaction–advection–diffusion equation in heterogeneous mediumA numerical method for solving variable‐order fractional diffusion equations using fractional‐order <scp>Taylor</scp> waveletsA new numerical strategy for solving nonlinear singular Emden-Fowler delay differential models with variable orderNumerical algorithm for a generalized form of Schnakenberg reaction-diffusion model with gene expression time delayA novel meshless method based on RBF for solving variable-order time fractional advection-diffusion-reaction equation in linear or nonlinear systemsCollocation method with Lagrange polynomials for variable‐order time‐fractional advection–diffusion problemsA new operational vector approach for time‐fractional subdiffusion equations of distributed order based on hybrid functionsA novel shifted Jacobi operational matrix method for nonlinear multi‐terms delay differential equations of fractional variable‐order with periodic and anti‐periodic conditionsSpace-dependent variable-order time-fractional wave equation: Existence and uniqueness of its weak solutionNumerical simulation of variable-order fractional differential equation of nonlinear Lane-Emden type appearing in astrophysicsApplications of variable-order fractional operators: a reviewA numerical approach for the system of nonlinear variable-order fractional Volterra integral equationsAn iterative approach for solving fractional optimal control problemsUnnamed ItemAPPROXIMATE SOLUTIONS FOR TIME-FRACTIONAL TWO-COMPONENT EVOLUTIONARY SYSTEM OF ORDER 2 USING COUPLED FRACTIONAL REDUCED DIFFERENTIAL TRANSFORM METHODJacobi Spectral Collocation Method for the Time Variable-Order Fractional Mobile-Immobile Advection-Dispersion Solute Transport ModelNumerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller DerivativeUnnamed ItemUnnamed ItemNEW RECURSIVE APPROXIMATIONS FOR VARIABLE-ORDER FRACTIONAL OPERATORS WITH APPLICATIONSA fractional-order Jacobi Tau method for a class of time-fractional PDEs with variable coefficientsThe convergence and stability analysis of the Jacobi collocation method for solving nonlinear fractional differential equations with integral boundary conditionsA unified difference-spectral method for time–space fractional diffusion equationsApproximate solutions for solving nonlinear variable-order fractional Riccati differential equationsSPACE-TIME SPECTRAL COLLOCATION ALGORITHM FOR THE VARIABLE-ORDER GALILEI INVARIANT ADVECTION DIFFUSION EQUATIONS WITH A NONLINEAR SOURCE TERMMoving front solutions of a time-fractional power-law fluid under gravityA highly accurate collocation algorithm for 1 + 1 and 2 + 1 fractional percolation equationsOn three-dimensional variable order time fractional chaotic system with nonsingular kernelModified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bézier curvesChebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana-Baleanu-Caputo variable-order fractional derivativeA fractional numerical study on a chronic hepatitis C virus infection model with immune responseNumerical simulation for fractional-order differential system of a glioblastoma multiforme and immune systemHaar wavelet collocation method for variable order fractional integro-differential equations with stability analysisAn accurate Chebyshev pseudospectral scheme for multi-dimensional parabolic problems with time delaysA new exponential Jacobi pseudospectral method for solving high-order ordinary differential equationsApproximate solution of linear and nonlinear fractional differential equations under \(m\)-point local and nonlocal boundary conditionsTwo shifted Jacobi-Gauss collocation schemes for solving two-dimensional variable-order fractional Rayleigh-Stokes problemApproximate analytical solutions of time fractional Whitham-Broer-Kaup equations by a residual power series methodAn operational matrix technique based on Chebyshev polynomials for solving mixed Volterra-Fredholm delay integro-differential equations of variable-orderNumerical identification of the fractional derivatives in the two-dimensional fractional cable equationA high order numerical scheme for variable order fractional ordinary differential equationA Jacobi spectral collocation method for solving multi-dimensional nonlinear fractional sub-diffusion equationsThe general solution for impulsive differential equations with Riemann-Liouville fractional-order \(q\in (1,2)\)A review of operational matrices and spectral techniques for fractional calculusOptical solitons in nonlinear directional couplers by sine-cosine function method and Bernoulli's equation approachA new fully discrete finite difference/element approximation for fractional cable equationA Jacobi Gauss-Lobatto and Gauss-Radau collocation algorithm for solving fractional Fokker-Planck equationsSoliton and soliton-like solutions to the modified Zakharov-Kuznetsov equation in nonlinear transmission lineThe lumped mass FEM for a time-fractional cable equationOn the new properties of Caputo-Fabrizio operator and its application in deriving shifted Legendre operational matrixAn improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equationsExact solution of certain time fractional nonlinear partial differential equationsNumerical algorithm for the variable-order Caputo fractional functional differential equationA two-grid finite element approximation for a nonlinear time-fractional Cable equationA fully spectral collocation approximation for multi-dimensional fractional Schrödinger equationsThe homogeneous balance of undetermined coefficients method and its applicationImproved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equationsA Lagrange regularized kernel method for solving multi-dimensional time-fractional heat equationsJacobi collocation approximation for solving multi-dimensional Volterra integral equationsNon-polynomial B-spline and shifted Jacobi spectral collocation techniques to solve time-fractional nonlinear coupled Burgers' equations numericallyLegendre wavelets optimization method for variable-order fractional Poisson equationSome identities involving the derivative of the first kind Chebyshev polynomialsSome identities involving Chebyshev polynomialsUnconditionally optimal error estimates of a linearized Galerkin method for nonlinear time fractional reaction-subdiffusion equationsAn efficient numerical technique for variable order time fractional nonlinear Klein-Gordon equationNew numerical approach for fractional variational problems using shifted Legendre orthonormal polynomialsAn integro quadratic spline approach for a class of variable-order fractional initial value problemsA novel adaptive order/parameter identification method for variable order systems application in viscoelastic soft tissue modelingAn efficient cubic spline approximation for variable-order fractional differential equations with time delayAn adaptive order/state estimator for linear systems with non-integer time-varying orderA fractional quadratic autocatalysis associated with chemical clock reactions involving linear inhibitionKing algorithm: a novel optimization approach based on variable-order fractional calculus with application in chaotic financial systemsAn optimization method based on the generalized Lucas polynomials for variable-order space-time fractional mobile-immobile advection-dispersion equation involving derivatives with non-singular kernelsA meshless method for solving two-dimensional variable-order time fractional advection-diffusion equationLocal discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equationOn Caputo-Hadamard type fractional impulsive hybrid systems with nonlinear fractional integral conditionsAn optimization method based on the generalized polynomials for nonlinear variable-order time fractional diffusion-wave equationExact combined traveling wave solutions and multi-symplectic structure of the variant Boussinesq-Whitham-Broer-Kaup type equationsEntropy analysis of systems exhibiting negative probabilitiesOn an accurate discretization of a variable-order fractional reaction-diffusion equationA meshless approach for solving nonlinear variable-order time fractional 2D Ginzburg-Landau equationOperational matrix approach for solving the variable-order nonlinear Galilei invariant advection-diffusion equationApproximation methods for solving fractional equationsA space-time spectral approximation for solving nonlinear variable-order fractional sine and Klein-Gordon differential equationsSome second-order \(\theta\) schemes combined with finite element method for nonlinear fractional cable equationA computational wavelet method for variable-order fractional model of dual phase lag bioheat equationAn improved tau method for the multi-dimensional fractional Rayleigh-Stokes problem for a heated generalized second grade fluidHighly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equationsUlam stability for nonlocal differential equations involving the Hilfer-Katugampola fractional derivativeGeneralized Lucas polynomial sequence approach for fractional differential equationsNumerical simulation of multi-dimensional distributed-order generalized Schrödinger equations



Cites Work


This page was built for publication: Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation