A review of operational matrices and spectral techniques for fractional calculus (Q328928)

scientific article; zbMATH DE number 6641890

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English	A review of operational matrices and spectral techniques for fractional calculus	scientific article; zbMATH DE number 6641890

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instance of

scholarly article

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title

A review of operational matrices and spectral techniques for fractional calculus (English)

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author

Taha M. Taha

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A. H. Bhrawy

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José A. Tenreiro Machado

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published in

Nonlinear Dynamics

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publication date

21 October 2016

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zbMATH Keywords

multi-term FDEs

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operational matrices

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Legendre polynomials

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Jacobi polynomials

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Chebyshev polynomials

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Bernstein polynomials

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generalized Laguerre polynomials

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modified generalized Laguerre polynomials

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tau method

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collocation method

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MaRDI profile type

Publication

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full work available at URL

https://doi.org/10.1007/s11071-015-2087-0

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cites work

The effect of fractional order in variable structure control

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Fractional order calculus: basic concepts and engineering applications

0 references

Approximate analytical solutions of the fractional-order Brusselator system using the polynomial least squares method

0 references

A mixed finite element method for a time-fractional fourth-order partial differential equation

0 references

Q4569476

0 references

Classification of traveling wave solutions for time-fractional fifth-order KdV-like equation

0 references

Numerical solution of distributed order fractional differential equations

0 references

A new predictor-corrector method for fractional differential equations

0 references

Numerical solution of fractional advection-diffusion equation with a nonlinear source term

0 references

An efficient method for solving fractional Hodgkin-Huxley model

0 references

A theorem on the existence of symmetries of fractional PDEs

0 references

On group invariant solutions of fractional order Burgers-Poisson equation

0 references

Stability analysis for HIV infection of \(\mathrm{CD}4^{+}\) T-cells by a fractional differential time-delay model with cure rate

0 references

Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann-Liouville derivative

0 references

On the operational solutions of fuzzy fractional differential equations

0 references

Approximating solutions of fully fuzzy linear systems: A financial case study

0 references

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

0 references

A predictor-corrector approach for the numerical solution of fractional differential equations

0 references

The operational matrix of fractional integration for shifted Chebyshev polynomials

0 references

Existence of extremal solutions for nonlinear fractional differential equation with nonlinear boundary conditions

0 references

Q5497334

0 references

Error estimate for the numerical solution of fractional reaction-subdiffusion process based on a meshless method

0 references

Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations

0 references

Fractional differential equations solved by using Mellin transform

0 references

Positive solutions for a class of singular fractional differential equation with infinite-point boundary value conditions

0 references

Numerical solution of nonlinear fractional differential equations by spline collocation methods

0 references

Existence of solutions of initial value problems for nonlinear fractional differential equations

0 references

An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein-Gordon equations

0 references

Identification of unknown parameters and orders via cuckoo search oriented statistically by differential evolution for noncommensurate fractional-order chaotic systems

0 references

Spectral Methods

0 references

Stable multi-domain spectral penalty methods for fractional partial differential equations

0 references

A multi-domain spectral method for time-fractional differential equations

0 references

Exponentially accurate spectral and spectral element methods for fractional ODEs

0 references

Application of Bessel functions for solving differential and integro-differential equations of the fractional order

0 references

Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations

0 references

Multiple positive solutions for nonlinear boundary value problem of fractional order differential equation with the Riemann-Liouville derivative

0 references

The use of radial basis functions (RBFs) collocation and RBF-QR methods for solving the coupled nonlinear sine-Gordon equations

0 references

A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations

0 references

Discrete-time orthogonal spline collocation method with application to two-dimensional fractional cable equation

0 references

A convergence analysis of the Jacobi spectral-collocation method for fractional integro-differential equations

0 references

Spectral collocation method for linear fractional integro-differential equations

0 references

A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order

0 references

A method based on the tau approach for the identification of a time-dependent coefficient in the heat equation subject to an extra measurement

0 references

Efficient Legendre spectral tau algorithm for solving the two-sided space–time Caputo fractional advection–dispersion equation

0 references

Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains

0 references

A unified Petrov-Galerkin spectral method for fractional PDEs

0 references

A meshless local Petrov-Galerkin method for the time-dependent Maxwell equations

0 references

Jacobi spectral Galerkin methods for fractional integro-differential equations

0 references

An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system

0 references

On the derivatives of Bernstein polynomials: an application for the solution of high even-order differential equations

0 references

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

0 references

On a singular integral equation including a set of multivariate polynomials suggested by Laguerre polynomials

0 references

Common and interlacing zeros of families of Laguerre~polynomials

0 references

Two efficient generalized Laguerre spectral algorithms for fractional initial value problems

0 references

A new modified generalized Laguerre operational matrix of fractional integration for solving fractional differential equations on the half line

0 references

A new operational matrix for solving fractional-order differential equations

0 references

A new Jacobi operational matrix: an application for solving fractional differential equations

0 references

Fractional-order Legendre functions for solving fractional-order differential equations

0 references

Numerical solution of the fractional partial differential equations by the two-dimensional fractional-order Legendre functions

0 references

An operational matrix based on Legendre polynomials for solving fuzzy fractional-order differential equations

0 references

Q3375569

0 references

Q5693171

0 references

The use of He's variational iteration method for solving the telegraph and fractional telegraph equations

0 references

Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

0 references

The construction of operational matrix of fractional derivatives using B-spline functions

0 references

A new operational matrix of fractional integration for shifted Jacobi polynomials

0 references

A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations

0 references

Reconstruction of exponentially rate of convergence to Legendre collocation solution of a class of fractional integro-differential equations

0 references

Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions

0 references

Oscillation of certain nonlinear fractional partial differential equation with damping term

0 references

Efficient numerical solution of the time fractional diffusion equation by mapping from its Brownian counterpart

0 references

Numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis

0 references

Q4061445

0 references

Q4023645

0 references

On the coefficients of differentiated expansions and derivatives of Jacobi polynomials

0 references

On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials

0 references

The special functions and their approximations. Vol. I, II

0 references

Bernstein operational matrix of fractional derivatives and its applications

0 references

Multi-order fractional differential equations and their numerical solution

0 references

New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions

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Identifiers

zbMATH Open document ID

1348.65106

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Mathematics Subject Classification ID

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10.1007/S11071-015-2087-0

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Sitelinks

Mathematics(1 entry)

mardi Publication:328928