Sürdürülebilir Kalkınma Amaçları
Yayınlar
- MakaleAçık Erişim2026Using the Laplace Transform Technique to Solve Hilfer Fractional Partial Differential Equations
Merdan, Mehmet; Şişman, Şeyma
This work derives analytical solutions to fractional partial differential equations utilizing the Hilfer fractional derivative through the use of the Laplace transform method. The suggested method offers a cohesive solution framework that concurrently retrieves the Liouville-Caputo and Riemann-Liouville formulations as particular instances for designated selections of the Hilfer parameters. Exact novel solution representations are derived for the fractional KdV, modified KdV, K(2,2), and Klein-Gordon equations under appropriate initial conditions, emphasizing the impact of fractional order and type parameters on wave propagation characteristics. The approach circumvents linearization or perturbation assumptions and demonstrates a rapid convergence rate. Numerical simulations and graphical representations produced with the Maple program corroborate the analytical findings and illustrate the efficacy and universality of the proposed method.
- MakaleAçık Erişim2025Analysis of Diabetes Complications Model With Time Delays
Merdan, Mehmet; Şişman, Şeyma
In this article, diabetes, a disease known to be influenced by genetic and environmental factors, is divided into two types: diabetes without complications (D) and diabetes with complications (C). The stability of the equilibrium points of this two-dimensional diabetes complication (DC) model, the D and C equations are studied by time delay. In addition, the behavior of the model is obtained with the help of the MATLAB package program.
- MakaleAçık Erişim2024Analysis of Random Difference Equations Using the Differential Transformation Method
Şişman, Şeyma; Merdan, Mehmet
The differential transformation method (DTM) is one of the best methods easily applied to linear and nonlinear difference equations with random coefficients. In this study, we apply the theorems related to the DTM to the given examples and investigate the behaviour of the approximate analytical solutions. The expected value, variance, coefficient of variation, and confidence intervals of the solutions of random difference equations obtained from discrete probability distributions such as uniform, geometric, Poisson, and binomial distributions will be calculated. Maple and MATLAB software packages are used to plot the solution graphs and also to interpret the solution behaviour.
- MakaleAçık Erişim2023On the solution of random linear difference equations with Laplace transform method
Şişman, Şeyma; Merdan, Mehmet
In this study, Laplace transformation, which is very important for solutions to initial value problems, is examined. To solve the initial value problem of a discrete-time equation, Laplace implements the conversion method. Here, Laplace transformation is used to obtain an approach to the solutions of random difference equations formed by randomizing components of deterministic difference equations. For random behavior of linear difference equations under random effects, uniform, geometric, binomial, Poisson, and Bernouilli distributions are used, and approximate expected value, variance, standard deviation, and confidence interval of equations obtained by Laplace transformation are calculated. The results were obtained through the Maple package program.
- MakaleAçık Erişim2022A Mathematical Model of Susceptible Diabetes Complication (SDC) Model in Discrete Time Fuzzy and Crisp Environment
Merdan, Mehmet; Şişman, Şeyma
In this study, we examined the mathematical model of the discrete-time equation system with susceptible diabetes complication (SDC), which is known to be caused by environmental and genetic factors in a fuzzy environment. From the diabetes complication (DC) model, the susceptible diabetes complication (SDC) model is being developed. It was obtained using definitions of how the behavior of this model changes in a fuzzy environment. A nonlinear differential equation system transforms the sensitive diabetes complication (SDC) model into a discrete time equation system. Stability analysis of the model with jury criterion was examined. In addition, numerical solutions and graphics of the analysis of the discrete model in fuzzy environment are obtained by using the MATLAB package program.
- MakaleYalnız künye2022DYNAMICAL ANALYSIS OF THE CONFORMABLE FRACTIONAL ORDER HOST-PARASITE MODEL
Şişman, Şeyma; Merdan, Mehmet
In this study, the differential equation system with a mathematical model of parasites is examined in cases where infection does not depend on transmission and defense, but on the level of infectivity and defense of the parasite and host. When discretization is applied to the differential equation, a two-dimensional discrete system is obtained in the range of t ∈ [n, n + 1] then the stability of the Neimark-Sacker bifurcation of the positive equilibrium point of this discrete system is investigated. Finally, MAPLE and MATLAB package program are used to show the accuracy of the results obtained.
- MakaleAçık Erişim2020Investigation of linear difference equations with random effects
Merdan, Mehmet; Şişman, Şeyma
In this study, random linear difference equations obtained by transforming the components of deterministic difference equations to random variables are investigated. Uniform, Bernoulli, binomial, negative binomial (or Pascal), geometric, hypergeometric and Poisson distributions have been used for the random effects for obtaining the random behavior of linear difference equations. The random version of the Z-transform, the RZ-transform, has been used to obtain an approximation for the random linear difference equation. Approximate expected values and variances are calculated by using the RZ-transform. The results have been obtained with Maple and are shown in graphs. It is shown that the random Z-transform is an effective tool for the investigation of random linear difference equations.
- MakaleYalnız künye2020ANALYSIS OF RANDOM DISCRETE TIME LOGISTIC MODEL
Merdan, Mehmet; Şişman, Şeyma
In this study, the behavior of the logistic difference model is investigated under random conditions using discrete probability distributions. The logistic difference model consists of parameters that depend on the population models to be used. For the study of random difference equation population models, the parameters are treated as random variables which constitutes the basis of the study. Random models were created using Uniform, Bernouilli, Binom, Negative Binomial (or Pascal), Geometric, Hypergeometric, Poisson distributions and their numerical characteristics are obtained through their simulations. Then, the results showing random numerical characteristics such as expected value, variance, standard deviation, coefficient of variation and confidence intervals were obtained with MATLAB package program. Analysis of random logistic difference model is given with the help of graphics and tables.