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Chebyshev differential quadrature for numerical solutions of third- and fourth-order singular perturbation problems
(Springer, 2019)
In this paper, linear and nonlinear singularly perturbed problems are studied by a numerical approach based on polynomial differential quadrature. The weighting coefficient matrix is acquired using Chebyshev polynomials. ...
Invariant and simulation analysis to the time fractional Abrahams - Tsuneto reaction diffusion system
(IOP Publishing, 2019)
In this work, symmetry analysis and numerical approximations to the time fractional Abrahams–Tsuneto reaction diffusion system (ATRDS) are discussed. We obtain point symmetries, similarity variables, similarity transformation ...
Solving the time - fractional schrodinger equation with the group preserving scheme
(The American Institute of Mathematical Sciences, 2019)
In this paper a powerful numerical scheme is proposed to gain the numerical solutions of the time-fractional Schrodinger equation: i C Dα 0+,tw(x, t) + ϑ ∂ 2w(x,t) ∂x2 + δ|w(x, t)| 2w(x, t) + P(x, t)w(x, t) = F(x, t), 0 < ...
On numerical solution of the time fractional advection - diffusion equation involving atangana - baleanu - caputo derivative
(Walter de Gruyter, 31.12.2019)
Abstract: A powerful algorithm is proposed to get the solutions of the time fractional Advection-Diffusion equation(TFADE): ABCD β 0 +,t u(x, t) = ζuxx(x, t) − κux(x, t) + F(x, t), 0 < β ≤ 1. The time-fractional derivative ...
Some new exact solutions for derivative nonlinear Schrödinger equation with the quintic non-Kerr nonlinearity
(World Scientific Publishing, 02.01.2020)
Recently, many researchers established various methods to construct optical solutions in the field of nonlinear optics because of optical solitons which shape the fundamental component to transport data from side to side ...
Families of exact solutions of Biswas-Milovic equation by an exponential rational function method
(Tbilisi Centre for Mathematical Sciences, 30.12.2019)
In this paper, we introduce generalized exponential rational function method (GERFM) to obtain an exact solutions for the Biswas-Milovic (BM) equation with quadratic-cubic and parabolic nonlinearities. A wide range of ...
The generalized gegenbauer - humberts wavelet for solving fractional differential equations
(Society of Thermal Engineers of Serbia, 2020)
In this paper we present a new method of wavelets, based on generalized Gegenbauer-Humberts polynomials, named generalized Gegenbauer-Humberts wavelets. The operational matrix of integration are derived. By using the ...
Optical solitons for the fractional (3 + 1) - dimensional NLSE with power law nonlinearities by using conformable derivatives
(Springer Nature Switzerland, 20.10.2020)
Abstract: In this paper, the process of the extended direct algebraic method (EDAM) is used to obtain the optical solitons in fractional (3 ? 1)-dimensional nonlinear Schrodinger equation through the conformable derivative. ...
Breather wave, lump - periodic solutions and some other interaction phenomena to the Caudrey – Dodd – Gibbon equation
(Springer Nature Switzerland, 12.07.2020)
Hirota’s bilinear method is used in this paper to obtain some breather wave and lumps solutions to the Caudrey–Dodd–Gibbon equation through the symbolic Mathematica 12 package. This equation is converted into its potential ...
Optical solitons and other solutions to the Radhakrishnan-Kundu-Lakshmanan equation
(Elsevier, 08.07.2021)
This paper studies the perturbed Radhakrishnan–Kundu–Lakshmanan (RKL) equation and its special form, the generalized RKL equation. Kerr law nonlinearity is considered for both equations. The Riccati-Bernoulli sub-ODE ...
