Mehmet Yavuz

Necmettin Erbakan Üniversitesi · Department of Mathematics and Computer Sciences

Mathematical models in epidemiology have been studied in the literature to understand the mechanism that underlies AIDS-related cancers, providing us with a better insight towards cancer immunity and viral oncogenesis. In this study, we propose a dynamical fractional order HIV-1 model in Caputo sense which involves the interactions between cancer c...

In this paper, we investigate novel solutions of fractional-order option pricing models and their fundamental mathematical analyses. The main novelties of the paper are the analysis of the existence and uniqueness of European-type option pricing models providing to give fundamental solutions to them and a discussion of the related analyses by consi...

Coronaviruses are a large family of viruses that cause different symptoms, from mild cold to severe respiratory distress, and they can be seen in different types of animals such as camels, cattle, cats and bats. Novel coronavirus called COVID-19 is a newly emerged virus that appeared in many countries of the world, but the actual source of the viru...

In the present paper, we implement a novel numerical method for solving differential equations with fractional variable-order in the Caputo sense to research the dynamics of a circulant Halvorsen system. Control laws are derived analytically to make synchronization of two identical commensurate Halvorsen systems with fractional variable-order time...

In the present paper, interactions between COVID-19 and diabetes are investigated using real data from Turkey. Firstly, a fractional order pandemic model is developed both to examine the spread of COVID-19 and its relationship with diabetes. In the model, diabetes with and without complications are adopted by considering their relationship with the...

In this paper, a non-singular SIR model with the Mittag-Leffler law is proposed. The nonlinear Beddington-DeAngelis infection rate and Holling type II treatment rate are used. The qualitative properties of the SIR model are discussed in detail. The local and global stability of the model are analyzed. Moreover, some conditions are developed to guar...

In this study, we propose new illustrative and effective modeling to point out the behaviors of the Hepatitis-B virus (Hepatitis-B). Not only do we consider the mathematical modeling, equilibria, stabilities, and existence-uniqueness analysis of the model, but also, we make numerical simulations by using the Adams-Bashforth numerical scheme. Howeve...

The core purpose of this work is the formulation of a mathematical model by dint of a new fractional modeling approach to study the dynamics of flow and heat transfer phenomena. This approach involves the incorporation of the Prabhakar fractional operator in mathematical analysis to transform the governing system from a conventional framework to a...

In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators. These have been intensively studied for mod...

In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators. These have been intensively studied for mod...

In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators. These have been intensively studied for mod...

Mathematical modelling has been widely used in many fields, especially in recent years. The applications of mathematical modelling in infectious diseases have shown that situations such as isolation, quarantine, vaccination and treatment are often necessary to eliminate most infectious diseases. In this study, a mathematical model of COVID-19 disea...

An investigation of the correlation between heart attack and the Omicron variant is presented in this paper using a novel mathematical model. In the model, in order to control both the number of infected individuals and the number of those with the Omicron variant, two control parameters are meant to be adjusted. Additionally, the model’s positivit...

This article explores and highlights the effect of stochasticity on the extinction behavior of a disease in a general epidemic model. Specifically, we consider a sophisticated dynamical model that combines logistic growth, quarantine strategy, media intrusion, and quadratic noise. The amalgamation of all these hypotheses makes our model more practi...

Recently, many illustrative studies have been performed on the mathematical modeling and analysis of COVID-19. Due to the uncertainty in the process of vaccination and its efficiency on the disease, there have not been taken enough studies into account yet. In this context, a mathematical model is developed to reveal the effects of vaccine treatmen...

Tuberculosis (TB) is an infectious disease with a high death rate compared to many infectious diseases. Therefore, many prominent studies have been done on the mathematical modeling and analysis of TB. In this study, an illustrative mathematical model is developed by considering the awareness parameter. In this context, two different treatment stra...

The current work is devoted to introduce a novel thermoelastic heat conduction model where the Moore-Gibson-Thompson (MGT) equation describes the heat equation. The constructed model is characterized by allowing limited velocities of heat wave propagation within the material, consistent with physical phenomena. The Green–Naghdi Type III model is im...

The present paper investigates the critical normal form coefficients for the one-parameter and two-parameter bifurcations of a discrete-time Bazykin-Berezovskaya prey-predator model. Based on the critical coefficients, it can be determined which scenario corresponds to each bifurcation. Further, for a better representation of the study, the complex...

The Navier–Stokes (NS) equations involving MHD effects with time-fractional derivatives are discussed in this paper. This paper investigates the local and global existence and uniqueness of the mild solution to the NS equations for the time fractional differential operator. In addition, we work on the regularity effects of such types of equations w...

In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stabilit...

This article develops a within-host viral kinetics model of SARS-CoV-2 under the Caputo fractional-order operator. We prove the results of the solution’s existence and uniqueness by using the Banach mapping contraction principle. Using the next-generation matrix method, we obtain the basic reproduction number. We analyze the model’s endemic and dis...

This issue is dedicated to the memory of Prof. Tenreiro Machado. https://dergipark.org.tr/en/pub/chaos/issue/64884

The study of thermal stratification has a broad scope of applications in solar engineering owing to its ability to predict the cases of achieving superior energy efficiency. This present communication focuses on the flow of a free convective MHD upper-convected Maxwell fluid in concert temperature-dependent viscosity, thermal conductivity across a...

The present research was developed to find out the effect of heated cylinder configurations in accordance with the magnetic field on the natural convective flow within a square cavity. In the cavity, four types of configurations—left bottom heated cylinder (LBC), right bottom heated cylinder (RBC), left top heated cylinder (LTC) and right top heate...

In this paper, some novel conditions for the stability results for a class of fractional-order quasi-linear impulsive integro-differential systems with multiple delays is discussed. First, the existence and uniqueness of mild solutions for the considered system is discussed using contraction mapping theorem. Then, novel conditions for Mittag–Leffle...

Optimization for all disciplines is very important and applicable. Optimization has played a key role in practical engineering problems. A novel hybrid meta-heuristic optimization algorithm that is based on Differential Evolution (DE), Gradient Evolution (GE) and Jumping Technique named Differential Gradient Evolution Plus (DGE+) are presented in t...

This article aims to develop a mathematical simulation of the steady mixed convective Darcy–Forchheimer flow of Williamson nanofluid over a linear stretchable surface. In addition, the effects of Cattaneo–Christov heat and mass flux, Brownian motion, activation energy, and thermophoresis are also studied. The novel aspect of this study is that it i...

This work proposes a qualitative study for the fractional second-grade fluid described by a fractional operator. The classical Caputo fractional operator is used in the investigations. The exact analytical solutions of the constructed problems for the proposed model are determined by using the Laplace transform method, which particularly includes t...

Listeriosis is one of the zoonotic diseases affecting most parts of the Sub-Saharan countries. The infection is often transmitted by eating and it can also pass by respiratory and direct contact. In this paper, a listeriosis mathematical model is formulated involving fractal-fractional orders in both Caputo and Atangana-Baleanu derivatives. Moreove...

In this study, a new approach to COVID-19 pandemic is presented. In this context, a fractional order pandemic model is developed to examine the spread of COVID-19 with and without Omicron variant and its relationship with heart attack using real data from the United Kingdom. In the model, heart attack is adopted by considering its relationship with...

In this article, unsteady free convective heat transport of copper-water nanofluid within a square-shaped enclosure with the dominance of non-uniform horizontal periodic magnetic effect is investigated numerically. Various nanofluids are also used to investigate temperature performance. The Brownian movement of nano-sized particles is included in t...

We reformulate a stochastic epidemic model consisting of four human classes. We show that there exists a unique positive solution to the proposed model. The stochastic basic re-production numberRs0is established. A stationary distribution (SD) under several conditions is obtained by incorporating stochastic Lyapunov function. The extinction for the...

In this study, we investigate a new fractional-order mathematical model which considers population dynamics among tumor cells-macrophage cells-active macrophage cells, and host cells involving the Caputo fractional derivative. Firstly, the stability of the positive steady state of the model is studied. Subsequently, the conditions for existence and...

The Korteweg–De Vries (KdV) equation has always provided a venue to study and generalizes diverse physical phenomena. The pivotal aim of the study is to analyze the behaviors of forced KdV equation describing the free surface critical flow over a hole by finding the solution with the help of q-homotopy analysis transform technique (q-HATT). he proj...

This research work is dedicated to studying the dynamics of a coupled plankton-oxygen model in the framework of three non-linear differential equations. As we know that the ocean dynamics have a firm impact on the global climate change and on the creation of the environment. Also, it is recorded that about 70% of the environmental oxygen is manufac...

In this paper, we have investigated some analytical, numerical and approximate-analytical methods by considering the time-fractional nonlinear fractional Burger-Fisher equation (FBFE). (1/G')-expansion method, finite difference method and Laplace perturbation method have been considered to solve the FBFE. Firstly, we have obtained the analytical so...

In the existent study, combined magneto-convection heat exchange in a driven enclosure having vertical fin was analyzed numerically. The finite element system-based GWR procedure was utilized to determine the flow model’s governing equations. A parametric inquiry was executed to review the influence of Richardson and Hartmann numbers on flow shape...

In this study, we consider the dynamics of the Babesiosis transmission on bovine populations and ticks. The most important role in the transmission of the parasite is the ticks from the Ixodidae family. The vector tick takes factors (merozoites in erythrocytes) from the diseased animal while sucking the blood. To model and investigate the transmiss...

In the existent study, combined magneto-convection heat exchange in a driven enclosure having vertical fin has been analyzed numerically. The finite element system-based GWR procedure is utilized to determine the flow model's governing equations. A parametric inquiry has been executed to review the influence of Richardson and Hartmann numbers on fl...

In the present paper, we implement a novel numerical method for solving differential equations with fractional variable-order in the Caputo sense to research the dynamics of a circulant Halvorsen system. Control laws are derived analytically to make synchronization of two identical commensurate Halvorsen systems with fractional variable-order time...

This study explores the fractional damped generalized regularized long‐wave equation in the sense of Caputo, Atangana‐Baleanu, and Caputo‐Fabrizio fractional derivatives. With the aid of fixed‐point theorem in the Atangana‐Baleanu fractional derivative with Mittag‐Leffler–type kernel, we show the existence and uniqueness of the solution to the damp...

Optimization for all disciplines is very important and applicable. Optimization has played a key role in practical engineering problems. A novel hybrid meta-heuristic optimization algorithm that is based on Differential Evolution (DE), Gradient Evolution (GE) and Jumping Technique named Differential Gradient Evolution Plus (DGE+) are presented in t...

In this article, the optimal auxiliary function method (OAFM) is extended to general partial differential equations (PDEs). Our proposed method is highly efficient and provides the means of controlling the approximate solution’s convergence. Illustrative examples are provided to prove the exceptional consistency of the PDEs’ analytical and numerica...

We investigate a couple of different financial/economic models based on market equilibrium and option pricing with three different fractional derivatives in this paper. We obtain the fundamental solutions of the models by Sumudu transform and Laplace transform. We demonstrate our results by illustrative figures to point out the difference between t...

In this article, we obtain oscillation conditions for second-order differential equation with neutral term. Our results extend, improve, and simplify some known results for neutral delay differential equations. Several effective and illustrative implementations are provided.

In this work, we present new oscillation conditions for the oscillation of the higher-order differential equations with the middle term. We obtain some oscillation criteria by a comparison method with first-order equations. The obtained results extend and simplify known conditions in the literature. Furthermore, examining the validity of the propos...

Fractional order differential equations are utilized for modeling many complicated physical and natural phenomena in nonlinear sciences and related fields. In this manuscript, the fractional-order Schrödinger-KdV equation in the sense of Atangana-Baleanu derivative is investigated. The Schrödinger-KdV equation demonstrates various types of wave pro...

Before going further with fractional derivative which is constructed by Rabotnov exponential kernel, there exist many questions that are not addressed. In this paper, we try to recapitulate all the fundamental calculus, which we can obtain with this new fractional operator. The problems in this paper are to determine the solutions of the fractional...

This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physi...

HIV is a topic that has been greatly discussed and researched due to its impact on human population. Many campaigns have been put into place, and people have been made aware of the various effects of the disease. This paper considers a fractional-order HIV epidemic model with the inclusion of prostitution in the population and its consequences on t...

This paper presents a fundamental solution method for nonlinear fractional regularized long-wave (RLW) models. Since analytical methods cannot be applied easily to solve such models, numerical or semianalytical methods have been extensively considered in the literature. In this paper, we suggest a solution method that is coupled with a kind of inte...

In this work, a fractional predator-prey model with the harvesting rate is considered. Besides the existence and uniqueness of the solution to the model, local stability and global stability are experienced. A novel discretization depending on the numerical discretization of the Riemann-Liouville integral was introduced and the corresponding numeri...

In this manuscript, two-hybrid techniques namely q-homotopy analysis Elzaki transform method (q-HAETM) and Iterative Elzaki transform method (IETM) have been applied for obtaining the numerical solutions of time-fractional Navier-Stokes equations in polar coordinate described in the Caputo sense. q-HAETM is the combination of the Homotopy Analysis...

In this manuscript, we have proposed a comparison based on newly defined fractional derivative operators which are called as Caputo-Fabrizio (CF) and Atangana-Baleanu (AB). In 2015, Caputo and Fabrizio established a new fractional operator by using exponential kernel. After one year, Atangana and Baleanu recommended a different-type fractional oper...

We consider a fractional-order nerve impulse model which is known as FitzHugh-Nagumo (F-N) model in this paper. Knowing the solutions of this model allows the management of the nerve impulses process. Especially, considering this model as fractional-order ensures to be able to analyze in detail because of the memory effect. In this context, first,...

Mathematical modelling of infectious diseases has shown that combinations of isolation, quarantine, vaccine and treatment are often necessary in order to eliminate most infectious diseases. Continuous mathematical models have been used to study the dynamics of infectious diseases within a human host and in the population. We have used in this study...

In this article, a spectral formulation is introduced for a Fractional Optimal Control Problem (FOCP) defined in spherical coordinates in the cases of half and complete axial symmetry. The dynamics of optimally controlled system are described by space-time fractional diffusion equation in terms of the Caputo and fractional Laplacian differentiation...

We investigated existence and uniqueness conditions of solutions of a nonlinear differential equation containing the Caputo-Fabrizio operator in Banach spaces. The mentioned derivative has been proposed by using the exponential decay law and hence it removed the computational complexities arising from the singular kernel functions inherit in the co...

This study investigates the fractional coupled viscous Burgers' equation under the Liouville-Caputo, Atangana-Baleanu and Yang-Srivastava-Machado fractional derivatives. With the help of fixed-point theorem, and using the Atangana-Baleanu fractional derivative with Mittag-Leffler kernel type kernel, we proved the existence and uniqueness of the stu...

In this paper, we consider some linear/nonlinear differential equations (DEs) containing conformable derivative operator (CDO). We obtain approximate solutions of these mentioned DEs in the form of infinite series which converges swiftly to its exact value by using separated homotopy method (SHM). Using the conformable operator in solutions of diff...

Countries aiming for sustainability in economic growth and development ensure the reliability of energy supplies. For countries to provide their energy needs uninterruptedly, it is important for domestic and renewable energy sources to be utilized. For this reason, the supply of reliable and sustainable energy has become an important issue that con...

In this chapter, a heat conduction equation in terms of the Caputo-Fabrizio derivative of order $0<\alpha \le 1$ is considered. Caputo-Fabrizio derivative is defined by a non-singular exponential decay kernel function. Thanks to this feature, it eliminates the computational difficulties arising from the singular power kernel functions of the tradit...

In this paper, we analyze the behaviours of two different fractional derivative operators defined in the last decade. One of them is defined with the normalized sinc function (NSF) and the other one is defined with the Mittag-Leffler function (MLF). Both of them have a non-singular kernel. The fractional derivative operator defined with the MLF is...

This study adresses two new numerical techniques for solving some interesting one-dimensional time-fractional partial differential equations (PDEs). We have introduced modified homotopy perturbation method in conformable sense (MHPMC) and Adomian decomposition method in conformable sense (ADMC) which improve the solutions for linear-nonlinear fract...

This paper proposes the fundamental solution of fractional order Cauchy heat problem by using Fourier and Laplace transforms. We use a new fractional derivative operator involving the normalized sinc function (NSF) without singular kernel. In the present paper we consider the integral transform techniques to obtain the solution of the fractional Ca...

In this paper, time-fractional advection-diffusion problem in terms of a new fractional derivative operator involving the normalized sinc function (NSF) is considered. This derivative operator is defined with nonsingular kernel. Therefore, it removes the computational complexities arising from the singular kernel functions inherit in the convention...

This study presents two new numerical techniques for solving time-fractional one-dimensional cable differential equation (FCE) modeling neuronal dynamics. We have introduced new formulations for the approximate-analytical solution of the FCE by using modified homotopy perturbation method defined with conformable operator (MHPMC) and reduced differe...