Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach-Adomian-meyers modified decomposition method
From MaRDI portal
Publication:440721
DOI10.1016/j.amc.2012.01.063zbMath1245.65087OpenAlexW2036788704MaRDI QIDQ440721
Jun-Sheng Duan, Temuer Chaolu, Randolph C. Rach
Publication date: 19 August 2012
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2012.01.063
power seriesAdomian decomposition methodmodified decomposition methodfractional differential equationsAdomian polynomialsAdomian-Rach theorem
Related Items
The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations, Abstract differential equations and Caputo fractional derivative, Local fractional Laplace variational iteration method for solving diffusion and wave equations on Cantor sets within local fractional operators, Analytical approximate solutions for differential equations with generalized Caputo-type fractional derivatives, Exact traveling wave solutions of the space-time fractional complex Ginzburg-Landau equation and the space-time fractional Phi-4 equation using reliable methods, Exact solutions of fractional order oscillation equation with two fractional derivative terms, Heat‐conduction in a semi‐infinite fractal bar using advanced Yang‐Fourier transforms, Analytical solutions of fractional differential equations using the convenient Adomian series, Approximate solutions of fractional Riccati equations using the Adomian decomposition method, Two reliable methods for solving the (3 + 1)-dimensional space-time fractional Jimbo-Miwa equation, The periodic solution of fractional oscillation equation with periodic input, Efficient analytic method for solving nonlinear fractional differential equations, \((N+1)\)-dimensional fractional reduced differential transform method for fractional order partial differential equations, Modified decomposition method with new inverse differential operators for solving singular nonlinear IVPs in first- and second-order PDEs arising in fluid mechanics, Local fractional series expansion method for solving wave and diffusion equations on Cantor sets, The zeros of the solutions of the fractional oscillation equation
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Adomian decomposition method for non-smooth initial value problems
- New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods
- A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations
- A fractional characteristic method for solving fractional partial differential equations
- An efficient algorithm for the multivariable Adomian polynomials
- Near-field and far-field approximations by the Adomian and asymptotic decomposition methods
- Convenient analytic recurrence algorithms for the Adomian polynomials
- New ideas for decomposing nonlinearities in differential equations
- New recurrence algorithms for the nonclassic Adomian polynomials
- Adomian decomposition: a tool for solving a system of fractional differential equations
- Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation
- Analysis of nonlinear fractional partial differential equations with the homotopy analysis method
- A convenient computational form for the Adomian polynomials
- Decomposition method for solving fractional Riccati differential equations
- A numerical scheme for the solution of multi-order fractional differential equations
- Generalized Taylor's formula
- Numerical algorithm based on Adomian decomposition for fractional differential equations
- Recurrence triangle for Adomian polynomials
- Adomian's decomposition method for solving an intermediate fractional advection-dispersion equation
- A new operational matrix for solving fractional-order differential equations
- Partial differential equations and solitary waves theory
- Anharmonic oscillator systems
- Numerical integration, analytic continuation, and decomposition
- Transformation of series
- Inhomogeneous nonlinear partial differential equations with variable coefficients
- Nonlinear transformation of series. II
- A modified decomposition
- Generalization of Adomian polynomials to functions of several variables
- Modified decomposition solution of nonlinear partial differential equations
- Fractals and fractional calculus in continuum mechanics
- On a Riemann-Liouville generalized Taylor's formula
- A reliable modification of Adomian decomposition method
- Solving frontier problems of physics: the decomposition method
- A reliable technique for solving the weakly singular second-kind Volterra-type integral equations
- Modified Adomian polynomials
- A mathematical model of Adomian polynomials
- A new algorithm for calculating Adomian polynomials for nonlinear operators
- On Mittag-Leffler-type functions in fractional evolution processes
- Compactons dispersive structures for variants of the \(K(n,n)\) and the KP equations
- Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion.
- Approximate analytical solution for seepage flow with fractional derivatives in porous media
- Nonlinear equations with mixed derivatives
- On composite nonlinearities and the decomposition method
- Detailed error analysis for a fractional Adams method
- Inversion of nonlinear stochastic operators
- Analytical approximate solutions for nonlinear fractional differential equations
- Concentration distribution of fractional anomalous diffusion caused by an instantaneous point source
- The Adomian method applied to some extraordinary differential equations
- Practical formulae for the calculus of multivariable Adomian polynomials
- Solution of non-integer order differential equations via the Adomian decomposition method
- Homotopy perturbation method for fractional KdV equation
- Solution of system of fractional differential equations by Adomian decomposition method
- Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results
- An improvement to an alternate algorithm for computing Adomian polynomials in special cases
- Solution of fractional differential equations by using differential transform method
- A method for obtaining bounds on eigenvalues and eigenfunctions by solving non-homogeneous integral equations
- An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method
- A new algorithm for calculating Adomian polynomials
- A developed new algorithm for evaluating Adomian polynomials
- Time- and space-fractional partial differential equations
- Reduced Polynomials and Their Generation in Adomian Decomposition Methods
- A new definition of the Adomian polynomials
- Time evolution and fluctuations of the probability density and entropy function for a class of nonlinear stochastic systems in mathematical physics
- The fractional diffusion equation
- An Efficient Methodology for the Physical Sciences
- A Fokker–Planck equation of fractional order with respect to time
- Modified decomposition solution of linear and nonlinear boundary-value problems
- Fractional Calculus: Integral and Differential Equations of Fractional Order
