A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations

By Shahrokh Esmaeili, Mostafa Shamsi. 2011

147 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7edfe7ee39ca1bb04eb156901067aaec1ace6af9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

1. Ali H. Bhrawy
2. Dumitru Băleanu
3. Mehdi Dehghan
4. Eid H. Doha
5. Hari M. Srivastava
6. Ş. Yüzbaşı
7. Mehrdad Lakestani
8. S. Ezz‐Eldien

In Numerical Analysis

1. Ali H. Bhrawy
2. Dumitru Băleanu
3. Mohsen Razzaghi
4. Eid H. Doha
5. Ş. Yüzbaşı
6. Mehdi Dehghan
7. Hari M. Srivastava
8. S. Ezz‐Eldien

Citations in the corpus

• Numerical solution of the Bagley–Torvik equation by the Bessel collocation method (2013, methodology): “method [8] Bashforth–Moulton method [41] 0 4.”
• Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials (2019, unknown): “+ (t − t0) n! u(t0), (21) then ||u(t) − ũn(t)|| = |||| (t − t0) (n + 1)! u(n+1)(ξ)|||| .”
• Numerical solution of the fractional Bagley‐Torvik equation by using hybrid functions approximation (2016, methodology): “Example 3b: In the second case, we suppose [12] A D B D C D 1.”
• A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials (2016, background): “Recent contributions in this field have been reported by Doha et al. (2013) and Esmaeili and Shamsi (2011).”
• Modified Galerkin algorithm for solving multitype fractional differential equations (2019, methodology): “Following the steps discussed in the previous section, we obtain a linear system similar to that given in (35).”
• THE CONSTRUCTION OF OPERATIONAL MATRIX OF FRACTIONAL DERIVATIVES USING B-SPLINE FUNCTIONS (2012, background): “We also refer the interested reader to [6,7,10,13,18,19,25,37,38,45].”
• The Müntz-Legendre Tau method for fractional differential equations (2016, methodology): “Comparison of obtained values between Pseudospectral method proposed in [14] and our method at x = 1 for example 3.”
• A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations (2013, methodology): “Recently, Esmaeili and Shamsi [27] introduced a direct solution technique for obtaining the spectral solution of a special family of fractional initial value problems using a pseudo-spectral method.”