arXiv subjects

Ali Akgül

Publications and source records attributed to Ali Akgül.

5 recordsLinked to original sources

arXiv2025

Harmful information spreading and its impact on vaccination campaigns modeled through fractal-fractional operators

Despite the huge efforts to develop and administer vaccines worldwide to cope with the COVID-19 pandemic, misinformation spreading through fake news in media and social networks about vaccination safety, make that people refuse to be vaccinated, which harms not only these people but also the whole population. In this work, we model the effects of harmful information spreading in immunization acquisition through vaccination. Our model is posed for several fractional derivative operators. We have conducted a comprehensive foundation analysis of this model for the different fractional derivatives. Additionally, we have incorporated a strength parameter that shows the combined impact of nonlinear and linear components within an epidemiological model. We have used the second derivative of the Lyapunov function to ascertain the detection of wave patterns within the vaccination dynamics.

math.DS↗

arXiv2018

Numerical solution of fractional Bratu type equations with Legendre reproducing kernel method

In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense. This method is predicated on iterative approach of reproducing kernel Hilbert space theory with shifted Legendre polynomials. Construction and convergence of iterative process are shown by orthogonal projection operator. Numerical results show that our method is effective and convenient for fractional Bratu type problem.

math.NA↗

arXiv2013

Approximate solutions for mhd squeezing fluid flow by reproducing kernel Hilbert space method

In this paper, a steady axisymmetric MHD flow of two dimensional in- compressible fluids has been investigated. Reproducing Kernel Hilbert Space Method (RKHSM) is implemented to obtain solution of reduced fourth order nonlinear boundary value problem. Numerical results have been compared with the resutls that obtained by the Range-Kutta Method (RK-4) and Optimal Homotopy Asymptotic Method (OHAM).

math.NA↗

arXiv2013

A numerical method based on the reproducing kernel Hilbert space method for the solution of fifth-order boundary-value problems

In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the equations have been obtained in terms of convergent series with easily computable components. We compare our results with spline methods, decomposition method, variational iteration method, Sinc-Galerkin method and homotopy perturbation methods. The comparison of the results with exact ones is made to confirm the validity and efficiency.

math.NA↗

arXiv2013

Numerical solution of one-dimensional Sine--Gordon equation using Reproducing Kernel Hilbert Space Method

In this paper, we propose a reproducing kernel Hilbert space method (RKHSM) for solving the sine--Gordon (SG) equation with initial and boundary conditions based on the reproducing kernel theory. Its exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have been studied to demonstrate the accuracy of the present method. The results obtained from the method are compared with the exact solutions and the earlier works. Results of numerical examples show that the presented method is simple and effective.

math.NA↗