EFFICIENT CHEBYSHEV SPECTRAL METHODS FOR SOLVING MULTI-TERM FRACTIONAL ORDERS DIFFERENTIAL EQUATIONS

By Eid H. Doha, Ali H. Bhrawy, S. Ezz‐Eldien. 2011

307 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6979ae742aaf46005daa84b4a9136aa3f488f5f2

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Citations in the corpus

Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials (2014, background): “Example 5 Consider the equation [55, 57] aDy.”
Numerical solution of the Bagley–Torvik equation by the Bessel collocation method (2013, methodology): “Also, some fractional differential equations have been solved by applying the various methods such as the pseudospectral scheme [8], the Chebyshev spectral methods [9], the operational matrix method [10], the Haar wavelet method [11], the Adomian decomposition method [12, 13], the Legendre wavelets ”
Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations (2013, methodology): “The authors in [16–18] constructed an efficient spectral method for the numerical approximation of fractional integrodifferential equations based on tau and pseudospectral methods.”
Numerical treatment for solving fractional Riccati differential equation (2013, unknown): “[27] as follows DðaÞ T nðxÞ 1⁄4 XN j1⁄40 Xn”
Modified Galerkin algorithm for solving multitype fractional differential equations (2019, background): “Then, (66) is equivalent to the following linear system ( Â − B̂ + μ D̂ ) C = F̂, (67) where C is given in the previous section, while the nonzero elements of the matrices Â, B̂, and D̂ are given explicitly in the following theorem.”
A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations (2013, methodology): “[15] proved a new formula expressing explicitly any fractional-order derivatives of shifted Chebyshev polynomials of any degree in terms of shifted Chebyshev polynomials themselves, and introduced spectral tau and collocation methods based on Chebyshev polynomials for solving multi-term linear and n”
Polynomial differential quadrature method for numerical solutions of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients (2014, methodology): “[6] proposed an efficient collocation methods based on Chebyshev polynomials for solving multi-term linear and nonlinear fractional differential equations subject to initial conditions.”