Fen - Edebiyat Fakültesi

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Citation Count: Mustafa, Ghulam...et al. (2020). "A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems", Mathematical Biosciences and Engineering, Vol. 17, No. 6, pp. 6659-6677.
A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems
(2020) Mustafa, Ghulam; Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C 2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.
Citation Count: Mahmoudi, Mohammad Reza...et al. (2020)."A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models", Symmetry-Basel, Vol. 12, No. 6.
A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models
(2020-06) Mahmoudi, Mohammad Reza; Maleki, Mohsen; Baleanu, Dumitru; Nguye, Vu-Thanh; Pho, Kim-Hung; 56389; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
In this paper, a Bayesian analysis of finite mixture autoregressive (MAR) models based on the assumption of scale mixtures of skew-normal (SMSN) innovations (called SMSN-MAR) is considered. This model is not simultaneously sensitive to outliers, as the celebrated SMSN distributions, because the proposed MAR model covers the lightly/heavily-tailed symmetric and asymmetric innovations. This model allows us to have robust inferences on some non-linear time series with skewness and heavy tails. Classical inferences about the mixture models have some problematic issues that can be solved using Bayesian approaches. The stochastic representation of the SMSN family allows us to develop a Bayesian analysis considering the informative prior distributions in the proposed model. Some simulations and real data are also presented to illustrate the usefulness of the proposed models.
Citation Count: Agarwal, Ravi Prakash;...et.al. (2022). "A Brief Overview and Survey of the Scientific Work by Feng Qi", Axioms, Vol.11, No.8.
A Brief Overview and Survey of the Scientific Work by Feng Qi
(2022-08) Agarwal, Ravi Prakash; Karapinar, Erdal; Kostić, Marko; Cao, Jian; Du, Wei-Shih; 19184; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
In the paper, the authors present a brief overview and survey of the scientific work by Chinese mathematician Feng Qi and his coauthors.
Citation Count: Ahmed, Idris...et al. (2023). "A Caputo-Fabrizio Fractional-Order Cholera Model And İts Sensitivity Analysis", Mathematical Modelling and Numerical Simulation with Applications, Vol. 3, No. 2, pp. 170-187.
A Caputo-Fabrizio Fractional-Order Cholera Model And İts Sensitivity Analysis
(2023-06-30) Ahmed, Idris; Akgül, Ali; Jarad, Fahd; Kumam, Poom; Nonlaopon, Kamsing; 234808; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
In recent years, the availability of advanced computational techniques has led to a growing emphasis on fractional-order derivatives. This development has enabled researchers to explore the intricate dynamics of various biological models by employing fractional-order derivatives instead of traditional integer-order derivatives. This paper proposes a Caputo-Fabrizio fractional-order cholera epidemic model. Fixed-point theorems are utilized to investigate the existence and uniqueness of solutions. A recent and effective numerical scheme is employed to demonstrate the model’s complex behaviors and highlight the advantages of fractional-order derivatives. Additionally, a sensitivity analysis is conducted to identify the most influential parameters
Citation Count: Baleanu, D...et al. (2018). A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel, Advances in Difference Equations.
A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel
(Pushpa Publishing House, 2018-10-04) Baleanu, Dumitru; Shiri, B.; Srivastava, H. M.; Al Qurashi, Maysaa Mohamed; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik - Bilgisayar Bölümü
In this paper, we solve a system of fractional differential equations within a fractional derivative involving the Mittag-Leffler kernel by using the spectral methods. We apply the Chebyshev polynomials as a base and obtain the necessary operational matrix of fractional integral using the Clenshaw-Curtis formula. By applying the operational matrix, we obtain a system of linear algebraic equations. The approximate solution is computed by solving this system. The regularity of the solution investigated and a convergence analysis is provided. Numerical examples are provided to show the effectiveness and efficiency of the method.
Citation Count: Baleanu, Dumitru; Krnic, Mario; Vukovic, Predrag (2021). "A class of fractal Hilbert-type inequalities obtained via Cantor-type spherical coordinates", Mathematical Methods in the Applied Sciences, Vol. 44, No. 7, pp. 6195-6208.
A class of fractal Hilbert-type inequalities obtained via Cantor-type spherical coordinates
(2021-05-15) Baleanu, Dumitru; Krnic, Mario; Vukovic, Predrag; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
We present a class of higher dimensional Hilbert-type inequalities on a fractal set (Double-struck capital R+alpha n)k. The crucial step in establishing our results are higher dimensional spherical coordinates on a fractal space. Further, we impose the corresponding conditions under which the constants appearing in the established Hilbert-type inequalities are the best possible. As an application, our results are compared with the previous results known from the literature.
Citation Count: Mustafa, Ghulam...et al. (2020). "A Class of Refinement Schemes With Two Shape Control Parameters", IEEE Access, Vol. 8, pp. 98316-98329.
A Class of Refinement Schemes With Two Shape Control Parameters
(2020) Mustafa, Ghulam; Hameed, Rabia; Baleanu, Dumitru; Mahmood, Ayesha; 56389; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
A subdivision scheme defines a smooth curve or surface as the limit of a sequence of successive refinements of given polygon or mesh. These schemes take polygons or meshes as inputs and produce smooth curves or surfaces as outputs. In this paper, a class of combine refinement schemes with two shape control parameters is presented. These even and odd rules of these schemes have complexity three and four respectively. The even rule is designed to modify the vertices of the given polygon, whereas the odd rule is designed to insert a new point between every edge of the given polygon. These schemes can produce high order of continuous shapes than existing combine binary and ternary family of schemes. It has been observed that the schemes have interpolating and approximating behaviors depending on the values of parameters. These schemes have an interproximate behavior in the case of non-uniform setting of the parameters. These schemes can be considered as the generalized version of some of the interpolating and B-spline schemes. The theoretical as well as the numerical and graphical analysis of the shapes produced by these schemes are also presented.
Citation Count: Sermutlu, Emre. "A close look at Newton–Cotes integration rules", Results in Nonlinear Analysis, Vol. 2, No. 2, pp. 48-60, (2019).
A close look at Newton–Cotes integration rules
(2019) Sermutlu, Emre; 17647; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
Newton–Cotes integration rules are the simplest methods in numerical integration. The main advantage of using these rules in quadrature software is ease of programming. In practice, only the lower orders are implemented or tested, because of the negative coefficients of higher orders. Most textbooks state it is not necessary to go beyond Boole’s 5-point rule. Explicit coefficients and error terms for higher orders are seldom given literature. Higher-order rules include negative coefficients therefore roundoff error increases while truncation error decreases as we increase the number of points. But is the optimal one really Simpson or Boole? In this paper, we list coefficients up to 19-points for both open and closed rules, derive the error terms using an elementary and intuitive method, and test the rules on a battery of functions to find the optimum all-round one.
Citation Count: Akın, Şeniz R. Kuşhan; Garcia, Caterina Bartomeu; Webster, Thomas J. (2021). "A comparative study of silicon nitride and SiAlON ceramics against E. coli", Ceramics International, Vol. 47, no. 2, pp. 1837-1843.
A comparative study of silicon nitride and SiAlON ceramics against E. coli
(2021-01-20) Akın, Şeniz R. Kuşhan; Garcia, Caterina Bartomeu; Webster, Thomas J.; 224219; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
In recent decades, due to some limitations from alumina (Al2O3) and zirconia (ZrO2), silicon nitride (Si3N4) has been investigated as a novel bioceramic material, mainly in situations where a bone replacement is required. Si3N4 ceramics and its derivative form, SiAlON, possess advantages in orthopedics due to their mechanical properties and biologically acceptable chemistry, which accelerates bone repair. However, biological applica- tions require additional properties, enabling stronger chemical bonding to the surrounding tissue for better fixation and the prevention of bacteria biofilm formation. Therefore, two commercial Si3N4 and SiAlON ceramics were investigated in this study and compared to each other according to their material properties (like wetting angles and surface chemistry) and their antibacterial behaviors using E. coli. Results provided evidence of a 15% reduction in E. coli colonization after just 24 h on Si3N4 compared to SiAlON which is impressive considering no antibiotics were used. Further, a mechanism of action is provided. In this manner, this study provides evidence that Si3N4 should be further studied for a wide range of antibacterial orthopedic, or other suitable biomaterial applications.
Citation Count: Baleanu, Dumitru; Agarwal, P., "A Composition Formula of the Pathway Integral Transform Operator", Note di Matematica, Vol. 34, No. 2, pp. 145-155, (2014).
A Composition Formula of the Pathway Integral Transform Operator
(University of Salento, 2014) Baleanu, Dumitru; Agarwal, Ravi P.; 56389; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
In the present paper, we aim at presenting composition formula of integral transform operator due to Nair, which is expressed in terms of the generalized Wright hypergeometric function, by inserting the generalized Bessel function of the first kind wv(z). Furthermore the special cases for the product of trigonometric functions are also consider. © 2014 Universitá del Salento.
Citation Count: Rashid, Saima;...et.al. (2022). "A comprehensive analysis of the stochastic fractal–fractional tuberculosis model via Mittag-Leffler kernel and white noise", Results in Physics, Vol.39.
A comprehensive analysis of the stochastic fractal–fractional tuberculosis model via Mittag-Leffler kernel and white noise
(2022-08) Rashid, Saima; Iqbal, Muhammad Kashif; Alshehri, Ahmed M.; Ashraf, Rehana; Jarad, Fahd; 234808; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
In this research, we develop a stochastic framework for analysing tuberculosis (TB) evolution that includes newborn immunization via the fractal–fractional (F–F) derivative in the Atangana–Baleanu sense. The population is divided into four groups by this system: susceptibility S(ξ), infectious I(ξ), immunized infants V(ξ), and restored R(ξ). The stochastic technique is used to describe and assess the invariant region, basic reproduction number, and local stability for disease-free equilibrium. This strategy has significant modelling difficulties since it ignores the unpredictability of the system phenomena. To prevent such problems, we convert the deterministic strategy to a randomized one, which seems recognized to have a vital influence by adding an element of authenticity and fractional approach. Owing to the model intricacies, we established the existence-uniqueness of the model and the extinction of infection was carried out. We conducted a number of experimental tests using the F–F derivative approach and obtained some intriguing modelling findings in terms of (i) varying fractional-order (φ) and fixing fractal-dimension (ω), (ii) varying ω and fixing φ, and (iii) varying both φ and ω, indicating that a combination of such a scheme can enhance infant vaccination and adequate intervention of infectious patients can give a significant boost.
Citation Count: Heydari, M. H.; Hosseininia, M.; Baleanu, D. (2023). "A Computational Approach Based On The Fractional Euler Functions And Chebyshev Cardinal Functions For Distributed-Order Time Fractional 2D Diffusion Equation", Alexandrıa Engineering Journal, Vol. 67, pp. 643-653.
A Computational Approach Based On The Fractional Euler Functions And Chebyshev Cardinal Functions For Distributed-Order Time Fractional 2D Diffusion Equation
(Alexandrıa Engineering Journal, 2023-03-15) Heydari, M. H.; Hosseininia, M.; Baleanu, D.; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
In this paper, the distributed-order time fractional diffusion equation is introduced and studied. The Caputo fractional derivative is utilized to define this distributed-order fractional derivative. A hybrid approach based on the fractional Euler functions and 2D Chebyshev cardinal functions is proposed to derive a numerical solution for the problem under consideration. It should be noted that the Chebyshev cardinal functions process many useful properties, such as orthogonal-ity, cardinality and spectral accuracy. To construct the hybrid method, fractional derivative oper-ational matrix of the fractional Euler functions and partial derivatives operational matrices of the 2D Chebyshev cardinal functions are obtained. Using the obtained operational matrices and the Gauss-Legendre quadrature formula as well as the collocation approach, an algebraic system of equations is derived instead of the main problem that can be solved easily. The accuracy of the approach is tested numerically by solving three examples. The reported results confirm that the established hybrid scheme is highly accurate in providing acceptable results
Citation Count: Khan, Faheem...et al. (2020). "A Computational Method for Subdivision Depth of Ternary Schemes", Mathematics, Vol. 8, No. 5.
A Computational Method for Subdivision Depth of Ternary Schemes
(2020-05) Khan, Faheem; Mustafa, Ghulam; Shahzad, Aamir; Baleanu, Dumitru; M. Al-Qurashi, Maysaa; 56389; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
Subdivision schemes are extensively used in scientific and practical applications to produce continuous shapes in an iterative way. This paper introduces a framework to compute subdivision depths of ternary schemes. We first use subdivision algorithm in terms of convolution to compute the error bounds between two successive polygons produced by refinement procedure of subdivision schemes. Then, a formula for computing bound between the polygon atk-th stage and the limiting polygon is derived. After that, we predict numerically the number of subdivision steps (depths) required for smooth limiting shape based on the demand of user specified error (distance) tolerance. In addition, extensive numerical experiments were carried out to check the numerical outcomes of this new framework. The proposed methods are more efficient than the method proposed by Song et al.
Citation Count: Al Qurashi, Maysaa; Rashid, Saima; Jarad, Fahd. (2022). "A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay", Mathematical Biosciences and Engineering, Vol.19, No.12, pp.12950-12980.
A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay
(2022) Al Qurashi, Maysaa; Rashid, Saima; Jarad, Fahd; 234808; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system’s equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order δ with constant fractal-dimension $, δ with changing $, and δ with changing both δ and $. White noise concentration has a significant impact on how bacterial infections are treated.
Citation Count: Baleanu, Dumitru...et al. (2020). "A coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives", Advances in Difference Equations, Vol. 2020, No. 1.
A coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives
(2020-05-27) Baleanu, Dumitru; Alzabut, J.; Jonnalagadda, J. M.; Adjabi, Y.; Matar, M. M.; 56389; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
In this paper, we study a coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations described by Atangana-Baleanu-Caputo (ABC for short) derivatives whose formulations are based on the notable Mittag-Leffler kernel. Prior to the main results, the equivalence of the coupled system to a nonlinear system of integral equations is proved. Once that has been done, we show in detail the existence-uniqueness and Ulam stability by the aid of fixed point theorems. Further, the continuous dependence of the solutions is extensively discussed. Some examples are given to illustrate the obtained results.
Citation Count: Güven, Ayşenur...at all (2021). "A Critical Review of the Joker Movie in the Context of Mahler's Separation-İndividuatin theory and PTSD", ETÜ Sosyal Bilimler Enstitüsü Dergisi, Vol. 13, pp. 122-148.
A Critical Review of the Joker Movie in the Context of Mahler's Separation-İndividuatin theory and PTSD
(2021) Güven, Ayşenur; Işık, Selin; Oya, Sera; Yaşar, Nuray; Topcu Bulut, Merve; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Psikoloji Bölümü
Bu çalışmada Mahler’in ayrılma-bireyleşme kuramı çerçevesinde Joker filmindeki Arthur Fleck karakterinin gelişim evreleri hakkında çıkarımlar yapılması, ilk 36 aylık deneyimlerinin Arthur’un duygu, düşünce ve kişilik gelişimindeki etkilerinin incelenmesi amaçlanmıştır. Mahler’in kuramına göre bireyin ilk altı ayı normal otistik ve normal ortakyaşamsal olmak üzere, birbirinin devamı ve tamamlayıcısı niteliğindeki iki kritik evreden oluşmaktadır. Devamında ise farklılaşma, alıştırma, yeniden yakınlaşma ve bireyliğin pekişmesi ve coşkusal nesne sürekliliğinin başlangıcı olmak üzere dört farklı altevreden oluşan ayrılma-bireyleşme süreci gelmektedir. Kişilik oluşumu sürecinde bu altevreler büyük önem taşımaktadır. Arthur’un narsistik ve madde kötüye kullanım tanısı almış olan annesi ile ilişkisi, baba kavramının eksikliği, çevresiyle olan etkileşimi ve toplum içinde görünür olma arzusu üzerinde durulmuştur. Çocukluk çağında istismar ve ihmale uğrayan, yetişkinlik çağında ise sistematik olarak psikolojik şiddete maruz kalmaya devam eden Arthur'un örseleyici yaşam öyküsü kimlik oluşumunu, sosyal uyumunu, kişilik gelişimini olumsuz etkilemiş ve örselenme sonrası gerginlik bozukluğu (ÖSGB) belirtilerinin oluşmasına yol açmıştır. Bahsedilen bilgiler ışığında Arthur Fleck karakteri, DSM-5 örselenme sonrası gerginlik bozukluğu tanı kriterlerinden faydalanılarak Mahler’in ayrılma-bireyleşme kuramı çerçevesinde incelenmiştir.
Citation Count: Talib, I. (2021). "A Decomposıtıon Algorıthm Coupled Wıth Operatıonal Matrıces Approach Wıth Applıcatıons To Fractıonal Dıfferentıal Equatıons", Thermal Science, Vol.25, No.2, pp.449-455.
A Decomposıtıon Algorıthm Coupled Wıth Operatıonal Matrıces Approach Wıth Applıcatıons To Fractıonal Dıfferentıal Equatıons
(2021) Talib, Imran; Alam, Md. Nur; Baleanu, Dumitru; Zaidi, Danish; 56389; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
In this article, we solve numerically the linear and non-linear fractional initial value problems of multiple orders by developing a numerical method that is based on the decomposition algorithm coupled with the operational matrices approach. By means of this, the fractional initial value problems of multiple orders are decomposed into a system of fractional initial value problems which are then solved by using the operational matrices approach. The efficiency and advantage of the developed numerical method are highlighted by comparing the results obtained otherwise in the literature. The construction of the new derivative operational matrix of fractional legendre function vectors in the Caputo sense is also a part of this research. As applications, we solve several fractional initial value problems of multiple orders. The numerical results are displayed in tables and plots.
Citation Count: Kumar, Pushpendra ...et.al. (2022). "A delayed plant disease model with Caputo fractional derivatives", Advances in Continuous and Discrete Models, Vol.2022, No.1.
A delayed plant disease model with Caputo fractional derivatives
(2022-12) Kumar, Pushpendra; Baleanu, Dumitru; Erturk, Vedat Suat; Inc, Mustafa; Govindaraj, V.; 56389; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington–DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams–Bashforth–Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.
Citation Count: Hosseini, K...et al. (2020). "A detailed study on a new (2+1)-dimensional mKdV equation involving the Caputo-Fabrizio time-fractional derivative", Advances in Difference Equations, Vol. 2020, No. 1.
A detailed study on a new (2+1)-dimensional mKdV equation involving the Caputo-Fabrizio time-fractional derivative
(2020-07-06) Hosseini, K.; Ilie, M.; Mirzazade, M.; Baleanu, Dumitru; 56389; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
The present article aims to present a comprehensive study on a nonlinear time-fractional model involving the Caputo-Fabrizio (CF) derivative. More explicitly, a new (2+1)-dimensional mKdV (2D-mKdV) equation involving the Caputo-Fabrizio time-fractional derivative is considered and an analytic approximation for it is retrieved through a systematic technique, called the homotopy analysis transform (HAT) method. Furthermore, after proving the Lipschitz condition for the kernel psi (x,y,t;u), the fixed-point theorem is formally utilized to demonstrate the existence and uniqueness of the solution of the new 2D-mKdV equation involving the CF time-fractional derivative. A detailed study finally is carried out to examine the effect of the Caputo-Fabrizio operator on the dynamics of the obtained analytic approximation.
Citation Count: Dehingia, Kaushik...et.al. (2022). "A Detailed Study on a Tumor Model with Delayed Growth of Pro-Tumor Macrophages", International Journal of Applied and Computational Mathematics, Vol.8, No.5
A Detailed Study on a Tumor Model with Delayed Growth of Pro-Tumor Macrophages
(2022-10) Dehingia, Kaushik; Hosseini, Kamyar; Salahshour, Soheil; Baleanu, D.; 56389; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
This paper investigates a tumor-macrophages interaction model with a discrete-time delay in the growth of pro-tumor M2 macrophages. The steady-state analysis of the governing model is performed around the tumor dominant steady-state and the interior steady-state. It is found that the tumor dominant steady-state is locally asymptotically stable under certain conditions, and the stability of the interior steady-state is affected by the discrete-time delay; as a result, the unstable system experiences a Hopf bifurcation and gets stabilized. Furthermore, the transversality conditions for the existence of Hopf bifurcations are derived. Several graphical representations in two and three-dimensional postures are given to examine the validity of the results provided in the current study.

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