6 papers
Periodic Fractional Control in Bioprocesses for Clean Water and Ecosystem Health
Kareem T. Elgindy, Muneerah Al Nuwairan, Liew Siaw Ching
This paper introduces a novel fractional-order chemostat model (FOCM) incorporating Caputo fractional derivative with sliding memory (CFDS) to capture microbial memory effects in b…
Hybrid Shifted Gegenbauer Integral-Pseudospectral Method for Solving Time-Fractional Benjamin-Bona-Mahony-Burgers Equation
Kareem T. Elgindy
This paper presents a high-order hybrid shifted Gegenbauer integral-pseudospectral (HSG-IPS) method for solving the time-fractional Benjamin-Bona-Mahony-Burgers (FBBMB) equation. A…
Sustainable Water Treatment through Fractional-Order Chemostat Modeling with Sliding Memory and Periodic Boundary Conditions: A Mathematical Framework for Clean Water and Sanitation
Kareem T. Elgindy
This work develops and analyzes a novel fractional-order chemostat system (FOCS) with a Caputo fractional derivative (CFD) featuring a sliding memory window and periodic boundary c…
Super-Exponential Approximation of the Riemann-Liouville Fractional Integral via Gegenbauer-Based Fractional Approximation Methods
Kareem T. Elgindy
This paper introduces a Gegenbauer-based fractional approximation (GBFA) method for high-precision approximation of the left Riemann-Liouville fractional integral (RLFI). By using…
The Numerical Approximation of Caputo Fractional Derivative of Higher Orders Using A Shifted Gegenbauer Pseudospectral Method: Two-Point Boundary Value Problems of the Bagley Torvik Type Case Study
Kareem T. Elgindy
This work presents a new framework for approximating Caputo fractional derivatives (FDs) of any positive order using a shifted Gegenbauer pseudospectral (SGPS) method. By transform…
Fourier-Gegenbauer Integral-Galerkin Method for Solving the Advection-Diffusion Equation With Periodic Boundary Conditions
Kareem T. Elgindy
This study presents the Fourier-Gegenbauer Integral-Galerkin (FGIG) method, a novel and efficient numerical framework for solving the one-dimensional advection-diffusion equation w…