A NEW JACOBI OPERATIONAL MATRIX: AN APPLICATION FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS

By Eid H. Doha, Ali H. Bhrawy, S. Ezz‐Eldien. 2012

343 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/a16cf99d596170e090951718e8b29411291a2281

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Citations in the corpus

An iterative approach for solving fractional optimal control problems (2018, neutral): “Spectral approximations have been used for solving FDEs by other authors too (see, for instance, Saadatmandi and Dehghan, 2010; Doha et al., 2012; Baleanu et al., 2013; Bhrawy and Zaky, 2015; Bhrawy et al., 2015c; Bhrawy et al. 2015e).”
A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations (2013, background): “Recently the Jacobi operational matrix of fractional derivatives has been developed in [19], to solve the multi-term FDEs.”
Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line (2014, methodology): “Doha et al. (2012) derived the Jacobi operational matrix of fractional derivatives which applied together with spectral tau and collocation methods for numerical solution of general linear and nonlinear multi-term FDEs, respectively.”
A review of operational matrices and spectral techniques for fractional calculus (2015, methodology): “As in a typical tau method (see [67,69]), we generate N − m + 1 linear algebraic equations by applying 〈RN (x), P L , j (x)〉 = ∫ L”
The Müntz-Legendre Tau method for fractional differential equations (2016, methodology): “L(2)-norm Errors N Müntz-Legendre Tau Method Legendre Tau Method[11] 5 1.”
New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions (2014, methodology): “[16] introduced the fractional derivatives of Jacobi operational matrix which was applied in combination with the Jacobi tau scheme for solving linear multi-term FDEs.”
Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations (2013, background): “Recently, using orthogonal polynomials have received considerable attention to solve FDE [22, 23].”
A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations (2015, background): “(For the proof, see [45].”
A numerical study of fractional relaxation–oscillation equations involving $$\psi $$ψ-Caputo fractional derivative (2018, background): “Next, it was extended to the fractional case by many authors, see for example [3,4,9,10,13,15,24], and the references therein.”
A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems (2017, methodology): “Recently, based on types of orthogonal polynomials, the operational matrix of fractional derivatives has been derived and used to approximate the solution of many types of fractional differential equations (see Doha et al., 2012, 2015; Bhrawy et al., 2014b, 2015a,b; Bhrawy and Zaky, 2015).”