Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation

By Ali H. Bhrawy, M. A. Zaky. Nonlinear dynamics, 2014

275 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/92c0e641c949c325b9f8f16a9b2d60e8102ab2e8

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Citations in the corpus

A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems (2017, methodology): “…types of fractional differential equations, namely the differential equations with arbitrary noninteger orders, were solved using numerical techniques based on some types of orthogonal polynomials (see Bhrawy and Baleanu, 2013; Doha et al., 2013; Bhrawy and Zaky, 2014; Bhrawy et al., 2014a).”
A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications (2019, methodology): “5) Bhrawy and Zaky [11] introduced Jacobi spectral collocation method as an efficient alternative approach to solve 2D VO fractional nonlinear cable equation in the following form”
A fractional‐order Jacobi Tau method for a class of time‐fractional PDEs with variable coefficients (2016, methodology): “In parallel, numerical methods for classical differential equations are developed for solving fractional PDEs, such as finite difference methods [11–13], finite element methods [14, 15], spectral methods [16, 17], and discontinuous Galerkin methods [18, 19].”
A numerical approach for solving a class of variable-order fractional functional integral equations (2018, methodology): “2013; Moghaddam and Machado 2017a), spectral methods (Bhrawy and Zaky 2014; Zayernouri and Karniadakis 2015) and spline interpolation methods (Yaghoobi et al.”
Trial solution technique to chiral nonlinear Schrodinger’s equation in (1$$+$$+2)-dimensions (2016, background): “(21) and integrating with resect to U, we get the following exact solution of Eq.”
An iterative approach for solving fractional optimal control problems (2018, unknown): “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).”