Solving nonlinear fractional partial differential equations using the homotopy analysis method

By Mehdi Dehghan, Jalil Manafian, Abbas Saadatmandi. 2010

678 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/0fefd7cd91b904dd25e9951ad29909c34b7c5d52

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. Mehdi Dehghan
3. M. A. Zaky
4. Mehrdad Lakestani
5. Yadollah Ordokhani
6. Jalil Manafian
7. Parisa Rahimkhani
8. Abbas Saadatmandi

In Numerical Analysis

1. Ali H. Bhrawy
2. Mehdi Dehghan
3. Mehrdad Lakestani
4. M. A. Zaky
5. Yadollah Ordokhani
6. Parisa Rahimkhani
7. Abbas Saadatmandi
8. Jalil Manafian

In Statistical and Nonlinear Physics

1. Jalil Manafian
2. M. A. Zaky
3. Mehrdad Lakestani
4. Ali H. Bhrawy
5. Mehdi Dehghan
6. Marwan Alquran
7. Abbas Saadatmandi
8. Yadollah Ordokhani

Citations in the corpus

• Application of the Exp‐function method for solving a partial differential equation arising in biology and population genetics (2011, methodology): “1) has attracted a considerable amount of researchwork, such as in Jone and Sleeman (2003), Fitzhugh (1961), Nagumo et al.”
• Analytical solution of time-fractional two-component evolutionary system of order 2 by residual power series method (2015, methodology): “Such methods are: Variational iteration method and multivariate Pade approximations [21], Iterative Laplace transform method [13], Adomian decomposition method [12, 17–19, 22], Homotopy analysis method [10, 11], Laplace-Homotopy perturbation method [14], Decomposition method [15] and Sumudu transfor”
• 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].”
• A Legendre collocation method for fractional integro-differential equations (2011, methodology): “…and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran, Iran Email: mdehghan@aut.ac.ir 2006; Momani and Noor, 2006), homotopy analysis method (Dehghan et al., 2010; Hashim et al., 2009), and collocation method (Rawashdeh, 2006; Saadatmandi and Dehghan, 2010a, b).”
• A numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditions (2018, methodology): “In [28], the homotopy analysis method is applied to solve nonlinear fractional partial differential equations.”
• New Improvement of the Expansion Methods for Solving the Generalized Fitzhugh-Nagumo Equation with Time-Dependent Coefficients (2015, methodology): “With the rapid development of nonlinear sciences based on computer algebraic system, many effective methods have been presented, such as the homotopy analysis method [3, 4], the variational iteration method [5–7], the homotopy perturbation method [8, 9], the sine-cosine method [10], the tanh-coth me”
• Gegenbauer spectral method for time‐fractional convection–diffusion equations with variable coefficients (2015, methodology): “Authors of [37] investigated the homotopy analysis method to solve nonlinear fractional partial differential equations such as fractional KdV, K(2, 2), Burgers, BBM-Burgers, cubic Boussinesq, coupled KdV, and Boussinesq-likeB(m,n)equations.”