Browsing by Author "Alshammari, Fehaid Salem"

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Novel Numerical Investigations of Some Problems Based on the Darcy-Forchheimer Model and Heat Transfer
(Mdpi, 2024) Akyildiz, Fahir Talay; Alshammari, Fehaid Salem; Tunc, Cemil
In this study, we introduced a new type of basis function and subsequently a Chebyshev delta shaped collocation method (CDSC). We then use this method to numerically investigate both the natural convective flow and heat transfer of nanofluids in a vertical rectangular duct on the basis of a Darcy-Brinkman-Forchheimer model and the electroosmosis-modulated Darcy-Forchheimer flow of Casson nanofluid over stretching sheets with Newtonian heating problems. The approximate solution is represented in terms of Chebyshev delta shaped basis functions. Novel error estimates for interpolating polynomials are derived. Computational experiments were carried out to corroborate the theoretical results and to compare the present method with the existing Chebyshev pseudospectral method. To demonstrate our proposed approach, we also compared the numerical solutions with analytic solutions of the Poisson equation. Computer simulations show that the proposed method is computationally cheap, fast, and spectrally accurate and more importantly the obtained approximate solution can easily be used by researchers in this field.
On the Existence of Solutions and Ulam-Type Stability for a Nonlinear Ψ-Hilfer Fractional-Order Delay Integro-Differential Equation
(MDPI, 2025) Tunc, Cemil; Alshammari, Fehaid Salem; Akyildiz, Fahir Talay
In this work, we address a nonlinear psi-Hilfer fractional-order Volterra integro-differential equation that incorporates n-multiple-variable time delays. Employing the psi-Hilfer fractional derivative operator, we investigate the existence of a unique solution, as well as the Ulam-Hyers-Rassias stability, semi-Ulam-Hyers-Rassias stability, and Ulam-Hyers stability of the proposed psi-Hilfer fractional-order Volterra integro-differential equation through the fixed-point approach. In this study, we enhance and generalize existing results in the literature on psi-Hilfer fractional-order Volterra integro-differential equations, both including and excluding single delay, by establishing new findings for nonlinear psi-Hilfer fractional-order Volterra integro-differential equations involving n-multiple-variable time delays. This study provides novel theoretical insights that deepen the qualitative understanding of fractional calculus.
Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations
(Mdpi, 2023) Tunc, Cemil; Alshammari, Fehaid Salem; Akyildiz, Fahir Talay
The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton's method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric.