# Fevzi ErdoganYuzuncu Yil University · Department of Mathematics

Fevzi Erdogan

PhD

## About

39

Publications

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927

Citations

## Publications

Publications (39)

In this paper, our intention is to investigate the blow-up theory for generalized auto-convolution Volterra integral equations (AVIEs). To accomplish this, we will consider certain conditions on the main equation. This will establish a framework for our analysis, ensuring that the solution of the equation exists uniquely and is positive. Firstly, w...

This study deals with singularly perturbed Volterra integro-differential equations with delay. Based on the properties of the exact solution, a hybrid difference scheme with appropriate quadrature rules on a Shishkin-type mesh is constructed. It is proved by using the truncation error estimate techniques and a discrete analogue of Grönwall’s inequa...

This paper presents an approach to the analysis and control of a class of affine nonlinear systems using neural networks. The proposed method combines the strengths of Lyapunov theory and neural network control to design a stable control law for a class of nonlinear systems that can be described by affine models and guarantees the asymptotic stabil...

In this paper, we propose a hybrid method for stabilizing nonlinear control systems based on a combination of neural networks and optimization techniques. Nonlinear systems are known to be difficult to control due to their complex and often unpredictable behavior. Our method is based on the combination of neural networks and optimization techniques...

In this paper, we designed a hybrid method based on the Nelder-Mead algorithm and feedforward neural network methods to solve ordinary differential equations. The idea behind using neural networks to solve differential equations is to use them as a function approximation to approximate the solution of the differential equation. Therefore, our propo...

In this paper, we propose an approach to solving nonlinear convex programming problems using recurrent neural networks (RNNs). Our method leverages the ability of RNNs to capture temporal dependencies and exploit the structure of the optimization problem to obtain efficient solutions. We show that by formulating the problem as a sequence-to-sequenc...

In the present study, a neuro-evolutionary scheme is presented for solving a class of singular singularly perturbed boundary value problems (SSP-BVPs) by manipulating the strength of feed-forward artificial neural networks (ANNs), global search particle swarm optimization (PSO) and local search interior-point algorithm (IPA), i.e., ANNs-PSO-IPA. An...

The purpose of this study is to introduce a stochastic computing solver for the multi-pantograph delay differential equation (MP-DDE). The MP-DDE is not easy to solve due to the singularities and pantograph terms. An advance computational intelligent paradigm is proposed to solve MP-DDE of the second kind by manipulating the procedures of the artif...

In this study, COVID-19 data in Turkey is investigated by Stochastic Differential Equation Modeling (SDEM). Firstly, parameters of SDE which occur in mentioned epidemic problem are estimated by using the maximum likelihood procedure. Then, we have obtained reasonable Stochastic Differential Equation (SDE) based on the given COVID-19 data. Moreover,...

The aim of this study is to design a layer structure of feed-forward artificial neural networks using the Morlet wavelet activation function for solving a class of pantograph differential Lane-Emden models. The Lane-Emden pantograph differential equation is one of the important kind of singular functional differential model. The numerical solutions...

In this study, a novel second-order prediction differential model is designed, and numerical solutions of this novel model are presented using the integrated strength of the Adams and explicit Runge–Kutta schemes. The idea of the present study comes to the mind to see the importance of delay differential equations. For verification of the novel des...

In this research, obtaining of approximate solution for fractional-order Burgers’ equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms. Then an iterative approach is constructed by using kernel functions. The convergence of this approach an...

The aim of this study is to determine the factors affecting PISA 2015
Mathematics literacy by using data mining methods such as Multilayer Perceptron Artificial Neural Networks and Random Forest.
Cause and effect relation within the context of the study was tried
to be discovered by means of data mining methods at the level of
deep learning. In ter...

The purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method...

In this study we investigated the singularly perturbed boundary value problems for semilinear reaction-difussion equations. We have introduced a basic and computational approach scheme based on Numerov’s type on uniform mesh. We indicated that the method is uniformly convergence, according to the discrete maximum norm, independently of the paramete...

A new computational intelligence numerical scheme is presented for the solution of second order nonlinear singular functional differential equations (FDEs) using artificial neural networks (ANNs), global operator genetic algorithms (GAs), efficient local operator interior-point algorithm (IPA), and the hybrid combination of GA-IPA. An unsupervised...

We present a new approach depending on reproducing kernel method (RKM) for time-fractional Kawahara equation with variable coefficient. This approach consists of obtaining an orthonormal basis function on specific Hilbert spaces. In this regard, some special Hilbert spaces are defined. Kernel functions of these special spaces are given and basis fu...

In this research, we present a hybrid method which combination of simplified reproducing kernel method (SRKM) and asymptotic expansion for solving singularly perturbed convection–diffusion problems. According to the hybrid method, firstly asymptotic expansion formed on boundary layer domain and then terminal value problem solved via SRKM on regular...

In this study, radial basis function artificial neural network (RBFN), which is one of the of data mining methods, was employed to determine the factors affecting PISA 2015 (Programme for International Student Assessment-PISA), Mathematics literacy. Mathematics literacy scores, which were made in categorical form with three level dependent variable...

In this article, we construct a novel iterative approach that depends on reproducing kernel method for Cahn–Allen equation with Caputo derivative. Representation of solution and convergence analysis are presented theoretically. Numerical results are given as tables and graphics with intent to show efficiency and power of method. The results demonst...

In this paper, we present an iterative reproducing kernel method for numerical solution of one dimensional fractional Burgers equation with variable coefficient. Convergence analysis is constructed theoretically. Numerical experiments show that approximate solution uniformly converges to exact solu- tion. The results demonstrate that the given meth...

This study deals with the singularly perturbed initial value problems for a quasilinear first-order delay differential equation. A quasilinearization technique for the appropriate delay differential problem theoretically and experimentally analyzed. The parameter uniform convergence is confirmed by numerical computations.

This study deals with the singularly perturbed initial value problems for a quasilinear first-order integro-differential equations with delay. A numerical method is generated on a grid that is constructed adaptively from a knowledge of the exact solution, which involves appropriate piecewise-uniform mesh on each time subinterval. An error analysis...

In this paper, a new method is given for solving singularly perturbed convection-diffusion problems. The present method is based on combining the asymptotic expansion method and the variational iteration method (VIM) with an auxiliary parameter. Numerical results show that the present method can provide very accurate numerical solutions not only in...

The purpose of this paper is to present a uniform finite difference method for the numerical solution of a second order singularly perturbed delay differential equation. The problem is solved by using a hybrid difference scheme on a Shishkin-type mesh. The method is shown to be uniformly convergent with respect to the perturbation parameter. Numeri...

With the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is used in constructing some new solutions to the two well-known nonlinear models, namely, the simplified modified Camassa-Holm and symmetric regularized long-wave equations. We obtain some novel complex, trigonometric and hyperbolic function solutions to th...

In this work, we consider the Bernoulli sub-equation function method for obtaining novel behaviors to the nonlinear evolution equation describing the dynamics of ionic currents along Microtubules. We obtain new results by using this technique. We plot two- and three-dimensional surfaces of the results by using Wolfram Mathematica 9. At the end of t...

In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x. The method do not require linearization or small perturbation. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of effici...

In this paper, we applied relatively new analytical techniques, the homotopy analysis method (HAM) and the Adomian’s decomposition method (ADM) for solving time-fractional Fornberg–Whitham equation. The homotopy analysis method contains the auxiliary parameter, which provides us with a simple way to adjust and control the convergence region of solu...

In this paper a nonlinear singularly perturbed initial problem is considered. The behavior of the exact solution and its derivatives is analyzed, and this leads to the construction of a Shishkin-type mesh. On this mesh a hybrid difference scheme is proposed, which is a combination of the second order difference schemes on the fine mesh and the midp...

This paper deals with singularly perturbed initial value problem for linear second-order delay differential equation. An exponentially
fitted difference scheme is constructed in an equidistant mesh, which gives first order uniform convergence in the discrete
maximum norm. The difference scheme is shown to be uniformly convergent to the continuous s...

This paper presents the approximate analytical solutions to solve the nonlinear Fornberg–
Whitham equation with fractional time derivative. By using initial values, explicit
solutions of the equations are solved by using a reliable algorithm like the variational iteration
method. The fractional derivatives are taken in the Caputo sense. The present...

This work deals with a singularly perturbed initial value problem for a quasi-linear second-order delay differential equation. An exponentially fitted difference scheme is constructed, in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm. Numerical results are also presented.

Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is...

This study deals with the singularly perturbed initial value problem for a quasilinear first-order delay differential equation.
A numerical method is generated on a grid that is constructed adaptively from a knowledge of the exact solution, which involves
appropriate piecewise-uniform mesh on each time subinterval. An error analysis shows that the...

This paper deals with a singularly perturbed initial value problem for linear first-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous...

This paper deals with the singularly perturbed initial value problem for a linear first-order delay differential equation. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh on each time subinterval. The difference scheme is shown to converge to the continuous solution uniformly with respect to t...

By using Lyapunov's function approach [13], some new results were established, which guarantee that the zero solution of non-linear vector differential equations of the form is unstable.