Mehmet Yavuz

Necmettin Erbakan Üniversitesi · Department of Mathematics and Computer Sciences

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...

The maintenance of free calcium in the cytoplasm is requisite for cell integrity and the regime of the multi-cellular process. Overproduction and degradation to manage this cellular entity produce offensive changes in tissue performance and as a result, commence fibrotic diseases. Thus, there is a necessity to know the cellular process for the incl...

In the present era, the plastic waste problem is a global challenge due to its massive production. The post-use of waste plastic influences the earth's environment, human life, marine life, and ocean. Thus there is a necessity to develop good strategies for the exclusion of plastic waste. Because of this, an extension is paid on the procedure of bu...

In this paper, we analyze the role of fear in a three-species non-delayed ecological model that examines the interactions among susceptible prey, infectious (diseased) prey, and predators within a food web. The prey population grows in a logistic manner until it achieves a carrying capacity, reflecting common population dynamics in the absence of p...

In this manuscript, we carried out a thorough analysis of the generalSIR model for epidemics. We broadened the model to includevaccination, treatment, and incidence rate. The vaccination rate isa testament to the alternatives made by individuals when it comesto receiving vaccinations and merging with the community of therecovered. The treatment rat...

The dissemination of a disease within a homogeneous population can typically be modeled and managed in a uniform fashion. Conversely, in non-homogeneous populations, it is essential to account for variations among subpopulations to achieve more precise predictive modeling and efficacious intervention strategies. In this study, we introduce and exam...

This study implements a minded approach to studying Ebola virus disease (EVD) by dividing the infected population into aware and unaware groups and including a hospitalized compartment. This offers a more detailed understanding of illness distribution, potential analyses, and the influence of public knowledge. The findings might improve healthcare...

The aim of this article is to help predict the course of lung cancer patients. To make this prediction as close to reality as possible, we used data from lung cancer patients receiving treatment at Erciyes University Hospitals in Kayseri, Turkey. First, we developed a mathematical model considering the cells in the microenvironment of lung cancer t...

The Middle East respiratory syndrome is a viral respiratory illness. It is caused by a common type of virus called coronavirus. The main objective of the present work, we develop a mathematical model for the transmission dynamics of the Middle East respiratory syndrome coronavirus (MERS-CoV) disease. To assess the transmissibility of the MERS-CoV,...

Mathematical modeling and system control are employed in many research problems, ranging from physical and chemical processes to biomathematics and life sciences [...]

The pathogens of dengue and chikungunya are transmitted by Aedes aegypti mosquitoes, presenting a significant likelihood of vectors and hosts being concurrently infected by both viruses. We present biological insights into the co-infection of chikungunya and dengue to elucidate the phenomena clearly. Therefore, we develop a mathematical model to co...

Following the two successful events, ICAME'21 and ICAME'18, we are pleased to announce that The 3rd International Conference on Applied Mathematics in Engineering (ICAME'24) will be held between June 26-28, 2024 in a hybrid format where both physical and remote participation will be allowed. The aim of this conference is to bring together leading r...

Colon cancer is a complex disease with genetically unstable cell lines. In order to better understand the complexity of colon cancer cells and their metastatic mechanisms, we develop a mathematical model in this study. The model is based on a system of fractional-order differential equations and Fractional-Cancer-Informed Neural Networks (FCINN). T...

The aim of this paper is to investigate a stochastic SIS (Susceptible, Infected, Susceptible) epidemic model in which the disease transmission coefficient and the death rate are subject to random disturbances. Using the convergence theorem for local martingales and solving the Fokker-Planck equation associated with the one-dimensional stochastic di...

The current manuscript investigates a model of the spread of polio under the condition of vaccination by using the novel modified Atangana-Baleanu-Caputo (mABC) fractional derivative. This problem has been studied for non-zero solutions under the modified operator. The series-type solution has been obtained through the application of a Laplace tran...

The hepatocyte cells regulate the wide range of liver function by moderating cellular activities such as lipid, protein metabolism, carbohydrate, and interact with other cells for proliferation and maintenance. In hepatocyte cells, the concentration of calcium uptake is quite extensive from various agonists such as active Gα${G_\alpha}$ subunit, ac...

This study investigates the dynamics of a discrete-time prey-predator model with a harvesting effect on the predator. During the analysis of the bifurcations at the interior fixed point, we find that there are some generic bifurcations, including fold, flip, Neimark-Sacker, and strong resonance bi- furcations. Using the normal form theory and the c...

In this paper, a new mathematical model of Hepatitis B is studied to investigate the transmission dynamics of the Hepatitis B virus (HBV). Many diseases can start from the womb and find us humans throughout our lives. These diseases are specific abnormal conditions that negatively affect the structure or function of all or part of an organism and d...

The International Conference on Computational Modeling and Sustainable Energy (ICCMSE 2023) will be held at Pandit Deendayal Energy University, Gandhinagar, Gujarat, India in collaboration with Necmettin Erbakan University, Konya, Turkiye and Youjiang Medical University for Nationalities, China during December 15-17, 2023. This conference is meant...

This study examines the dynamics of a stochastic prey–predator model using a functional response function driven by Lévy noise and a mixed Holling-II and Beddington–DeAngelis functional response. The proposed model presents a computational analysis between two prey and one predator population dynamics. First, we show that the suggested model admits...

Predictive Modeling and Control Strategies for the Transmission of Middle East Respiratory Syndrome Coronavirus. Math. Comput. Appl. 2023, 28, 98. Abstract: The Middle East respiratory syndrome coronavirus (MERS-CoV) is a highly infectious respiratory illness that poses a significant threat to public health. Understanding the transmission dynamics...

Compared to many infectious diseases, tuberculosis has a high mortality rate. Because of this, a great deal of illustrative research has been done on the modeling and study of tuberculosis using mathematics. In this work, a mathematical model is created by taking into account the underlying presumptions of this disease. One of the main novelties of...

Water pollution is a critical global concern that demands ongoing scrutiny and revision of water resource policies at all levels to safeguard a healthy living environment. In this study, we focus on examining the dynamics of a fractional-order model involving three interconnected lakes, utilizing the Caputo differential operator. The aim is to inve...

In this paper, a fractional-order coinfection model for the transmission dynamics of COVID-19 and tuberculosis is presented. The positivity and boundedness of the proposed coinfection model are derived. The equilibria and basic reproduction number of the COVID-19 sub-model, Tuberculosis sub-model, and COVID-19 and Tuberculosis coinfection model are...

Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number of the model to examine its airborne transmissio...

The Murnaghan model of the doubly dispersive equation, which is well-known in the field of materials research, is taken into consideration in this work. This equation is resolved using three different mathematical methods. The analytical method can produce traveling wave solutions by utilizing the wave transform. While bright-dark soliton and brigh...

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...

Mathematical modelling and simulation in biophysics and its applications in terms of both theoretical and biological/physical/ecological point of view arise in a number of research problems ranging from physical and chemical processes to biomathematics and life science. As known, the modeling of a biophysical system requires the analysis of the dif...

This paper presents an investigation into the relationship between heart attacks and the Omicron variant, employing a novel mathematical model. The model incorporates two adjustable control parameters to manage the number of infected individuals and individuals with the Omicron variant. The study examines the model's positivity and boundedness, eva...

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...

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.