Browsing by Author "Latif, Mohamed S. Abdel"

Now showing 1 - 4 of 4

Citation - WoS: 14
Citation - Scopus: 16
The Invariant Subspace Method for Solving Nonlinear Fractional Partial Differential Equations With Generalized Fractional Derivatives
(Springeropen, 2020) Kader, Abass H. Abdel; Baleanu, Dumitru; Latif, Mohamed S. Abdel; Abdel Latif, Mohamed S.; Abdel Kader, Abass H.
In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter-Saxton equation, a time fractional nonlinear diffusion equation, a time fractional thin-film equation, the fractional Whitman-Broer-Kaup-type equation, and a system of time fractional diffusion equations.
Citation - WoS: 5
Rouge Wave, W-Shaped, Bright, and Dark Soliton Solutions for a Generalized Quasi-1d Bose-Einstein Condensate System With Local M-Derivative
(Springer, 2022) Latif, Mohamed S. Abdel; Baleanu, Dumitru; Kader, Abass H. Abdel
In this paper, a generalized quasi-1D Bose-Einstein condensate system with contact repulsion and dipole-dipole attraction (QBECS) and with the local M-derivative of order alpha is introduced. Using similarity transformation, the generalized QBECS is transformed into the same system but with constant coefficients under certain conditions. Finally, the travelling wave transformation is used for getting rogue waves and soliton solutions for the original equation. The effect of the fractional order alpha on the wave profile is discussed using some figures.
Citation - WoS: 2
Some New Exact Solutions for a Generalized Variable Coeffi- Cients Kdv Equation
(int Scientific Research Publications, 2023) Kader, Abass H. Abdel; Latif, Mohamed S. Abdel; Baleanu, Dumitru; El Sonbaty, Amr; Rajagopalan, R.
In this paper, the variable coefficients KdV equation with general power nonlinearities is proposed. Firstly, it is transformed into a generalized KdV equation with constant coefficients using a point transformation. Then, the traveling wave transformation is utilized to transform the obtained constant coefficients generalized KdV equation into a generalized ordinary differential equation. We give a classification for the obtained generalized ordinary differential equation using a suitable integrating factor. Some new solutions are obtained for the generalized KdV equation with constant coefficients. All the obtained solutions in this paper for the variable coefficients KdV equation with general power nonlinearities are new.
Citation - WoS: 1
Citation - Scopus: 1
Studying Heat Conduction in a Sphere Considering Hybrid Fractional Derivative Operator
(Vinca inst Nuclear Sci, 2022) Latif, Mohamed S. Abdel; Baleanu, Dumitru; Kader, Abass H. Abdel
In this paper, the fractional heat equation in a sphere with hybrid fractional derivative operator is investigated. The heat conduction is considered in the case of central symmetry with heat absorption. The closed form solution in the form of three parameter Mittag-Leffler function is obtained for two Dirichlet boundary value problems. The joint finite sine Fourier-Laplace transform is used for solving these two problems. The dynamics of the heat transfer in the sphere is illustrated through some numerical examples and figures.