A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula

From MaRDI portal
Publication:939511

DOI10.1016/j.cam.2007.07.033zbMath1148.65099OpenAlexW1989047470MaRDI QIDQ939511

Shaher Momani, Zaid M. Odibat

Publication date: 22 August 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.07.033




Related Items (76)

Numerical solution of fractional differential equations using hybrid Bernoulli polynomials and block pulse functionsMODIFIED FINITE ELEMENT NUMERICAL METHOD FOR SOLVING CONFORMABLE SPACE-TIME FRACTIONAL NONLINEAR PARTIAL DIFFERENTIAL EQUATIONSApproximation of solutions of polynomial partial differential equations in two independent variablesStability for a class of semilinear fractional stochastic integral equationsMatrix method based on the second kind Chebyshev polynomials for solving time fractional diffusion-wave equationsSolving the time-fractional diffusion equation via sinc-Haar collocation methodFractional variational iteration method versus Adomian's decomposition method in some fractional partial differential equationsRETRACTED: The general (vector) solutions of such linear (coupled) matrix fractional differential equations by using Kronecker structuresApplication of tan(φ(ξ)/2)-expansion method to burgers and foam drainage equationsAn analytical and approximate solution for nonlinear Volterra partial integro-differential equations with a weakly singular kernel using the fractional differential transform methodNumerical Multistep Approach for Solving Fractional Partial Differential EquationsA numeric-analytic method for approximating a giving up smoking model containing fractional derivativesSolving the fractional nonlinear Bloch system using the multi-step generalized differential transform methodApproximate analytic solutions of time-fractional Hirota-Satsuma coupled KdV equation and coupled MKdV equationA constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equationFast implicit integration factor method for nonlinear space Riesz fractional reaction-diffusion equationsApplication of multistep generalized differential transform method for the solutions of the fractional-order Chua's systemNumerical simulation of multidimensional nonlinear fractional Ginzburg-Landau equationsAdaptive multi-step differential transformation method to solving nonlinear differential equationsCompacton and solitary pattern solutions for nonlinear dispersive KdV-type equations involving Jumarie's fractional derivativeOn numerical solution to fractional nonlinear oscillatory equationsA study on the convergence conditions of generalized differential transform methodNumerical solutions for solving a class of fractional optimal control problems via fixed-point approachApproximate analytic solution of fractional heat-like and wave-like equations with variable coefficients using the differential transforms methodOn Chaotic Behavior of Temperature Distribution in a Heat ExchangerA new method for solving variable coefficients fractional differential equations based on a hybrid of Bernoulli polynomials and block pulse functionsAdaptation of differential transform method for the numeric-analytic solution of fractional-order Rössler chaotic and hyperchaotic systemsOn the convergence of a new reliable algorithm for solving multi-order fractional differential equationsOn Legendre polynomial approximation with the VIM or HAM for numerical treatment of nonlinear fractional differential equationsA reproducing kernel Hilbert space method for solving integro-differential equations of fractional orderExistence of solutions for multi point boundary value problems for fractional differential equationsPositive solutions for multi-point boundary value problems for nonlinear fractional differential equationsApplication of the multistep generalized differential transform method to solve a time-fractional enzyme kineticsStatus of the differential transformation methodApproximation methods for solving fractional equationsVariational iteration method for the time-fractional Fornberg-Whitham equationThe use of cubic splines in the numerical solution of fractional differential equationsAn approximate solution of a fractional order differential equation model of human T-cell lymphotropic virus I (HTLV-I) infection of T-cellsApplication of Legendre wavelets for solving fractional differential equationsTau approximate solution of fractional partial differential equationsAnalytical study of fractional-order multiple chaotic FitzHugh-Nagumo neurons model using multistep generalized differential transform methodEpidemic model of leptospirosis containing fractional orderThe solution of the time-fractional diffusion equation by the generalized differential transform methodSolutions of Some Linear Fractional Partial Differential Equations in Mathematical PhysicsA Green's function approach for the numerical solution of a class of fractional reaction-diffusion equationsQuadratic spline solution for boundary value problem of fractional orderNumerical solution of the nonlinear conformable space-time fractional partial differential equationsApplying Legendre wavelet method with Tikhonov regularization for one-dimensional time-fractional diffusion equationsEfficient analytic method for solving nonlinear fractional differential equationsComputational method for solving space fractional Fisher's nonlinear equationA numerical approach for the Riesz space-fractional Fisher' equation in two-dimensionsRobust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional orderMultistep generalized transformation method applied to solving equations of discrete and continuous time-fractional enzyme kineticsA reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equationsEfficient multi-step differential transform method: theory and its application to nonlinear oscillatorsOn the asymptotic integration of a class of sublinear fractional differential equationsExistence and uniqueness of the solutions for a class of nonlinear fractional order partial differential equations with delayImproved \((G'/G)\)-expansion method for the space and time fractional foam drainage and KdV equationsNumerical solution of the fractional partial differential equations by the two-dimensional fractional-order Legendre functionsA multi-step differential transform method and application to non-chaotic or chaotic systemsAnalytic study on linear systems of fractional differential equationsHomotopy analysis method for solving multi-term linear and nonlinear diffusion-wave equations of fractional orderNumerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform methodApproximate analytical solution for the fractional modified Kdv by differential transform methodBivariate generalized Taylor's formula and its applications to solve FPDEsAlternative variational iteration method for solving the time-fractional Fornberg-Whitham equationComparing two numerical methods for approximating a new giving up smoking model involving fractional order derivativesThe homotopy analysis method for solving the time-fractional Fornberg-Whitham equation and comparison with Adomian's decomposition methodThe Nehari manifold and its application to a fractional boundary value problemNonlocal boundary value problems for hyperbolic equations with a Caputo fractional derivativeVariational approximate solutions of fractional nonlinear nonhomogeneous equations with Laplace transformComputational solution of a fractional integro-differential equationPositive solutions for class of state dependent boundary value problems with fractional order differential operatorsA new method for solving fractional partial differential equationsComputing eigenelements of boundary value problems with fractional derivativesA stable explicitly solvable numerical method for the Riesz fractional advection-dispersion equations



Cites Work


This page was built for publication: A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula