Numerical studies for a multi-order fractional differential equation

By Nasser Hassan Sweilam, Mohamed M. Khader, R. Al-Bar. 2007

310 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/68fa34a8570c163ceb675c029e0f419a2f4c0c6f

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Citations in the corpus

THE CONSTRUCTION OF OPERATIONAL MATRIX OF FRACTIONAL DERIVATIVES USING B-SPLINE FUNCTIONS (2012, methodology): “There are several techniques for solving such equations like Adomian decomposition method [14,27,30,35,43], He’s variational iteration method [17,29,31], homotopy perturbation method [29,40], homotopy analysis method [16], collocation method [34], Galerkin method [12] and other methods [21,24].”
A Legendre collocation method for fractional integro-differential equations (2011, methodology): “…equations have been given such as variational iteration method (Inc, 2008), homotopy perturbation method (Jafari and Momani, 2007; Sweilam et al., 2007), Adomian’s decomposition method (Jafari and Daftardar-Gejji, 1Department of Mathematics, Faculty of Science, University of…”
Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line (2014, methodology): “…methods have been developed in order to solve fractional differential equations (FDEs) (see, for example, Daftardar-Gejji and Jafari, 2007; Sweilam et al., 2007; Golbabai and Sayevand, 2010; Momani and Ibrahim, 2010; Cheng and Chu, 2011; Ibrahim and Darus, 2011; Wu, 2011; Dhaigude and…”
A new operational matrix for solving fractional-order differential equations (2010, methodology): “We next consider the following nonlinear initial value problem [21,28] D3y(x)+ D 5 2 y(x)+ y2(x) = x4, y(0) = y(0) = 0, y(0) = 2.”
Numerical treatment for solving fractional Riccati differential equation (2013, methodology): “Several numerical and approximate methods to solve FDEs have been given such as variational iteration method [6], homotopy perturbation method [9], Adomian decomposition method [10], homotopy analysis method [11] and collocation method [12–15].”
Variational iteration method for fractional heat- and wave-like equations (2009, methodology): “[36] solved heat-like and wave-like equations with variable coefficients by VIM, Sweilam [27] used VIM to solve multi-order FDEs, and in general.”