Journal ArticleDOI
A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations
Ali H. Bhrawy,Mahmoud A. Zaky +1 more
Reads0
Chats0
TLDR
This paper proposes and analyzes an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions using shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives.About:
This article is published in Journal of Computational Physics.The article was published on 2015-01-15. It has received 277 citations till now. The article focuses on the topics: Jacobi method & Fractional calculus.read more
Citations
More filters
Journal ArticleDOI
Optical solitons in nonlinear directional couplers by sine–cosine function method and Bernoulli’s equation approach
Mohammad Mirzazadeh,Mostafa Eslami,Essaid Zerrad,Mohammad F. Mahmood,Anjan Biswas,Anjan Biswas,Milivoj R. Belic +6 more
TL;DR: In this article, the sinecosine function method and Bernoulli's equation approach were used to obtain soliton solutions to optical couplers by two methods, i.e., sine-cosine method and sine equation approach.
Journal ArticleDOI
A review of operational matrices and spectral techniques for fractional calculus
TL;DR: In this paper, the authors used operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials.
Journal ArticleDOI
A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
TL;DR: The proposed collocation scheme, both in temporal and spatial discretizations, is successfully extended to solve the two-dimensional TFSE, demonstrating the utility and high accuracy of the new approach over other numerical methods.
Journal ArticleDOI
Trial solution technique to chiral nonlinear Schrodinger’s equation in (1+2)-dimensions
TL;DR: In this paper, the authors applied the trial solution technique to chiral nonlinear Schrodinger's equation in (1 + $$+$$ 2)-dimensions, which led to solitons and other solutions to the model.
Journal ArticleDOI
An improved collocation method for multi-dimensional spacetime variable-order fractional Schrdinger equations
Ali H. Bhrawy,M.A. Zaky +1 more
TL;DR: In this paper, a high order numerical scheme for multi-dimensional variable-order fractional Schrdinger equations is proposed, which is based on the shifted Jacobi polynomials (SJPs).
References
More filters
Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Posted Content
Orthogonal Polynomials
TL;DR: In this paper, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed and orthogonality on the unit circle is not discussed.
Book
Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.