All Stories

  1. A Unified Gegenbauer Framework for Arbitrary-Order Riemann-Liouville Fractional Integrals with Tunable Endpoint Regularity

    Article • January 2026, MDPI AG

    Dr Kareem T Elgindy

  2. A Lucas Operational Matrix Method for Solving Nonlinear Fractional Two‐Dimensional Partial Volterra Integral Equations

    Article • International Journal of Mathematics and Mathematical Sciences, January 2026, Wiley

    Dr Kareem T Elgindy

  3. Sustainable Water Treatment Through Fractional-Order Chemostat Modeling with Sliding Memory and Periodic Boundary Conditions: A Mathematical Framework for Clean Water and Sanitation

    Article • Fractal and Fractional, December 2025, MDPI AG

    Dr Kareem T Elgindy

  4. Fourier–Gegenbauer Integral Galerkin Method for Solving the Advection–Diffusion Equation with Periodic Boundary Conditions

    Article • Computation, September 2025, MDPI AG

    Dr Kareem T Elgindy

  5. Numerical Solutions of Fractional Weakly Singular Two-Dimensional Partial Volterra Integral Equations Using Euler Wavelets

    Article • Mathematics, August 2025, MDPI AG

    Dr Kareem T Elgindy

  6. Hybrid Shifted Gegenbauer Integral–Pseudospectral Method for Solving Time-Fractional Benjamin–Bona–Mahony–Burgers Equation

    Article • Mathematics, August 2025, MDPI AG

    Dr Kareem T Elgindy

  7. Super-Exponential Approximation of the Riemann–Liouville Fractional Integral via Gegenbauer-Based Fractional Approximation Methods

    Article • Algorithms, June 2025, MDPI AG

    Dr Kareem T Elgindy

  8. The Numerical Approximation of Caputo Fractional Derivatives of Higher Orders Using a Shifted Gegenbauer Pseudospectral Method: A Case Study of Two-Point Boundary Value Problems of the Bagley–Torvik Type

    Article • Mathematics, May 2025, MDPI AG

    Dr Kareem T Elgindy

  9. Numerical solution of nonlinear periodic optimal control problems using a Fourier integral pseudospectral method

    Article • Journal of Process Control, December 2024, Elsevier

    Dr Kareem T Elgindy

  10. Fourier–Gegenbauer pseudospectral method for solving periodic fractional optimal control problems

    Article • Mathematics and Computers in Simulation, November 2024, Elsevier

    Dr Kareem T Elgindy

  11. Optimal Periodic Control of Unmanned Aerial Vehicles Based on Fourier Integral Pseudospectral and Edge-Detection Methods

    Article • Unmanned Systems, September 2024, World Scientific Pub Co Pte Lt

    Dr Kareem T Elgindy

  12. Fourier–Gegenbauer Pseudospectral Method for Solving Periodic Higher-Order Fractional Optimal Control Problems

    Article • International Journal of Computational Methods, June 2024, World Scientific Pub Co Pte Lt

    Dr Kareem T Elgindy

  13. Direct integral pseudospectral and integral spectral methods for solving a class of infinite horizon optimal output feedback control problems using rational and exponential Gegenbauer polynomials

    Article • Mathematics and Computers in Simulation, May 2024, Elsevier

    Dr Kareem T Elgindy

  14. Fourier-Gegenbauer pseudospectral method for solving time-dependent one-dimensional fractional partial differential equations with variable coefficients and periodic solutions

    Article • Mathematics and Computers in Simulation, April 2024, Elsevier

    Dr Kareem T Elgindy

  15. New optimal periodic control policy for the optimal periodic performance of a chemostat using a Fourier–Gegenbauer-based predictor-corrector method

    Article • Journal of Process Control, July 2023, Elsevier

    Dr Kareem T Elgindy

  16. A direct integral pseudospectral method for solving a class of infinite-horizon optimal control problems using Gegenbauer polynomials and certain parametric maps

    Article • AIMS Mathematics, January 2023, American Institute of Mathematical Sciences (AIMS)

    Dr Kareem T Elgindy

  17. High-order numerical solution of viscous Burgers' equation using an extended Cole–Hopf barycentric Gegenbauer integral pseudospectral method

    Article • International Journal of Computer Mathematics, May 2021, Taylor & Francis

    Dr Kareem T Elgindy

  18. High-order Gegenbauer integral spectral element method integrated with an adaptive Chebyshev optimization strategy for solving linear singularly perturbed differential equations

    Article • Journal of Computational and Applied Mathematics, January 2020, Elsevier

    Dr Kareem T Elgindy

  19. Distributed optimal control of viscous Burgers' equation via a high‐order, linearization, integral, nodal discontinuous Gegenbauer‐Galerkin method

    Article • Optimal Control Applications and Methods, October 2019, Wiley

    Dr Kareem T Elgindy

  20. A high-order embedded domain method combining a Predictor-Corrector-Fourier-Continuation-Gram method with an integral Fourier pseudospectral collocation method for solving linear partial differential equations in complex domains

    Article • Journal of Computational and Applied Mathematics, March 2019, Elsevier

    Dr Kareem T Elgindy

  21. High-order integral nodal discontinuous Gegenbauer-Galerkin method for solving viscous Burgers' equation

    Article • International Journal of Computer Mathematics, November 2018, Taylor & Francis

    Dr Kareem T Elgindy, Bulent Karasozen

  22. High-order numerical solution of viscous Burgers' equation using a Cole-Hopf barycentric Gegenbauer integral pseudospectral method

    Article • Mathematical Methods in the Applied Sciences, July 2018, Wiley

    Dr Kareem T Elgindy

  23. High-order shifted Gegenbauer integral pseudo-spectral method for solving differential equations of Lane–Emden type

    Article • Applied Numerical Mathematics, June 2018, Elsevier

    Dr Kareem T Elgindy

  24. Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted Gegenbauer integral pseudospectral method

    Article • Journal of Industrial & Management Optimization, June 2017, American Institute of Mathematical Sciences (AIMS)

    Dr Kareem T Elgindy

  25. High-order adaptive Gegenbauer integral spectral element method for solving non-linear optimal control problems

    Article • Optimization, March 2017, Taylor & Francis

    Dr Kareem T Elgindy

  26. High-order, stable, and efficient pseudospectral method using barycentric Gegenbauer quadratures

    Article • Applied Numerical Mathematics, March 2017, Elsevier

    Dr Kareem T Elgindy

  27. Optimization via Chebyshev polynomials

    Article • Korean Journal of Computational & Applied Mathematics, January 2017, Springer Science + Business Media

    Dr Kareem T Elgindy

  28. High-order numerical solution of second-order one-dimensional hyperbolic telegraph equation

    Article • Numerical Methods for Partial Differential Equations, July 2015, Wiley

    Dr Kareem T Elgindy

  29. GEGENBAUER COLLOCATION INTEGRATION METHODS: ADVANCES IN COMPUTATIONAL OPTIMAL CONTROL THEORY

    Article • Bulletin of the Australian Mathematical Society, February 2014, Cambridge University Press

    Dr Kareem T Elgindy

  30. Fast, accurate, and small-scale direct trajectory optimization using a Gegenbauer transcription method

    Article • Journal of Computational and Applied Mathematics, October 2013, Elsevier

    Dr Kareem T Elgindy

  31. Optimal Gegenbauer quadrature over arbitrary integration nodes

    Article • Journal of Computational and Applied Mathematics, April 2013, Elsevier

    Dr Kareem T Elgindy

  32. Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices

    Article • Journal of Computational and Applied Mathematics, January 2013, Elsevier

    Dr Kareem T Elgindy

  33. On the optimization of Gegenbauer operational matrix of integration

    Article • Advances in Computational Mathematics, December 2012, Springer Science + Business Media

    Dr Kareem T Elgindy

  34. Generation of higher order pseudospectral integration matrices

    Article • Applied Mathematics and Computation, March 2009, Elsevier

    Dr Kareem T Elgindy

  35. A new robust line search technique based on Chebyshev polynomials

    Article • Applied Mathematics and Computation, December 2008, Elsevier

    Dr Kareem T Elgindy