Hassan A. Zedan
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View article: Spectral Treatment of the Fractional Bratu Equation via Shifted Lucas Polynomials: A Precise Collocation Approach with Error Quantification
Spectral Treatment of the Fractional Bratu Equation via Shifted Lucas Polynomials: A Precise Collocation Approach with Error Quantification Open
This paper introduces a novel spectral collocation method based on shifted Lucas polynomials for solving the fractional Bratu differential equation with nonhomogeneous Dirichlet boundary conditions. The method employs a homogenization stra…
View article: Two-dimensional wavelets collocation method for time-space fractional Schrödinger system
Two-dimensional wavelets collocation method for time-space fractional Schrödinger system Open
This paper proposes a wavelet method to obtain a numerical solution to the time-space fractional Schrödinger equation. With Caputo fractional derivatives, two dimensional Legendre wavelets and their operational matrix with the collocation …
View article: Shifted Chebyshev spectral method for the approximate solution of multi-term fractional differential equation
Shifted Chebyshev spectral method for the approximate solution of multi-term fractional differential equation Open
In this paper, we state and prove a new formula expressing explicitly the derivatives of shifted Chebyshev polynomials of any degree and for any fractional-order in terms of shifted Chebyshev polynomials themselves. We give a comparison of…
View article: Lie group method and fractional differential equations
Lie group method and fractional differential equations Open
In this paper, Lie group method is applied to investigate and solve some classes of nonlinear fractional differential equations.In addition, we use the obtained symmetries to induce exact solutions for the equations under consideration.
View article: New Solutions for System of Fractional Integro‐Differential Equations and Abel’s Integral Equations by Chebyshev Spectral Method
New Solutions for System of Fractional Integro‐Differential Equations and Abel’s Integral Equations by Chebyshev Spectral Method Open
Chebyshev spectral method based on operational matrix is applied to both systems of fractional integro‐differential equations and Abel’s integral equations. Some test problems, for which the exact solution is known, are considered. Numeric…
View article: Description of the Magnetic Field and Divergence of Multisolenoid Aharonov-Bohm Potential
Description of the Magnetic Field and Divergence of Multisolenoid Aharonov-Bohm Potential Open
Explicit formulas for the magnetic field and divergence of multisolenoid Aharonov-Bohm potential are obtained; the mathematical essence of this potential is explained. It is shown that the magnetic field and divergence of this potential ar…