Numerical comparison of methods for solving linear differential equations of fractional order

By Shaher Momani, Zaid M. Odibat. 2007

432 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5491fb441749cbe83b4758d710f1c10d11ecc892

How researchers see this paper

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

In Applied Mathematics

1. Ji-Huan He
2. Mehdi Dehghan
3. Dumitru Băleanu
4. Shaher Momani
5. V. S. Erturk
6. Fatemeh Shakeri
7. Hossein Jafari
8. Xu-Hong Wu

In Modeling and Simulation

1. Mehdi Dehghan
2. Ji-Huan He
3. Shaher Momani
4. Dumitru Băleanu
5. Zaid M. Odibat
6. Xu-Hong Wu
7. Fatemeh Shakeri
8. Hossein Jafari

In Numerical Analysis

1. Mehdi Dehghan
2. Ji-Huan He
3. Shaher Momani
4. Zaid M. Odibat
5. Dumitru Băleanu
6. Fatemeh Shakeri
7. Xu-Hong Wu
8. V. S. Erturk

Citations in the corpus

• Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem (2008, methodology): “Odibat and Momani [27] applied the method to nonlinear differential equations of fractional order with great success, see [6,26].”
• SOLVING MULTI-TERM ORDERS FRACTIONAL DIFFERENTIAL EQUATIONS BY OPERATIONAL MATRICES OF BPs WITH CONVERGENCE ANALYSIS (2013, background): “960047 0 t BPs (ours) BPFs [12] ADM [11] FDTM [9] Exact 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9”
• A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials (2012, methodology): “[17] S. Momani, Z. Odibat, Numerical comparison of methods for solving linear differential equations of fractional order.”
• Variational iteration method—Some recent results and new interpretations (2007, positive): “Starting from pioneering ideas going back to Inokuti–Sekine–Mura method [16], the method has matured into a fully fledged theory thanks to the effects of many researchers, notably, Wazwaz [27], Draganescu [6,7], Abdou and Soliman [1–4,23,24], Odibat and Momani [19–22], Bildik [5], Marinca [17], Mogh”
• Variational iteration method: New development and applications (2007, methodology): “For example, Abbasbandy applied the variational iteration method to Riemann–Liouville’s fractional derivatives [10], Draganescu and his colleagues to nonlinear vibration with fractional damping [11], Momani and his colleagues applied the method to fluid mechanics where the fractional derivative was ”