Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems
(2020) Baleanu, Dumitru; Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; 56389
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.
A Caputo-Fabrizio Fractional-Order Cholera Model And İts Sensitivity Analysis
(2023) Jarad, Fahd; Akgül, Ali; Jarad, Fahd; Kumam, Poom; Nonlaopon, Kamsing; 234808
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
A class of fractal Hilbert-type inequalities obtained via Cantor-type spherical coordinates
(2021) Baleanu, Dumitru; Krnic, Mario; Vukovic, Predrag; 56389
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.
A class of time-fractional Dirac type operators
(2021) Baleanu, Dumitru; Restrepo, Joel E.; Suragan, Durvudkhan; 56389
By using a Witt basis, a new class of time-fractional Dirac type operators with time-variable coefficients is introduced. These operators lead to considering a wide range of fractional Cauchy problems. Solutions of the considered general fractional Cauchy problems are given explicitly. The representations of the solutions can be used efficiently for analytic and computational purposes. We apply the obtained representation of a solution to recover a variable coefficient solution of an inverse fractional Cauchy problem. Some concrete examples are given to show the diversity of the obtained results. (c) 2020 Elsevier Ltd. All rights reserved.
A comparative study of silicon nitride and SiAlON ceramics against E. coli
(2021) Akın, Şeniz R. Kuşhan; Garcia, Caterina Bartomeu; Webster, Thomas J.; 224219
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.
A comparative study on biodegradation and mechanical properties of pressureless infiltrated Ti/Ti6Al4V-Mg composites
(Elsevier Science BV, 2016) Esen, Ziya; Karakaş, Mustafa Serdar; Karakaş, Mustafa Serdar; 52373; 47423
The mechanical response and biodegradation behavior of pressureless Mg-infiltrated Ti-Mg and Ti6Al4V-Mg composites were investigated by compression and simulated body fluid immersion tests, respectively. Prior porous preforms were surrounded uniformly with magnesium as a result of infiltration and the resultant composites were free of secondary phases and intermetallics. Although the composites' compressive strengths were superior compared to bone, both displayed elastic moduli similar to that of cortical bone and had higher ductility with respect to their starting porous forms. However, Ti-Mg composites were unable to preserve their mechanical stabilities during in-vitro tests such that they fractured in multiple locations within 15 days of immersion. The pressure generated by H-2 due to rapid corrosion of magnesium caused failure of the Ti-Mg composites through sintering necks. On the other hand, the galvanic effect seen in Ti6Al4V-Mg was less severe compared to that of Ti-Mg. The degradation rate of magnesium in Ti6Al4V-Mg was slower, and the composites were observed to be mechanically stable and preserved their integrities over the entire 25-day immersion test. Both composites showed bioinert and biodegradable characteristics during immersion tests and magnesium preferentially corroded leaving porosity behind while Ti/Ti6Al4V remained as a permanent scaffold. The porosity created by degradation of magnesium was refilled by new globular agglomerates. Mg(OH)(2) and CaHPO4 phases were encountered during immersion tests while MgCl2 was detected during only the first 5 days. Both composites were classified as bioactive since the precipitation of CaHPO4 phase is known to be precursor of hydroxyapatite formation, an essential requirement for an artificial material to bond to living bone. (C) 2016 Elsevier Ltd. All rights reserved.
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) Heydari, M. H.; Hosseininia, M.; Baleanu, D.; 56389
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
A direct numerical solution of time-delay fractional optimal control problems by using Chelyshkov wavelets
(Sage Publications LTD, 2019) Baleanu, Dumitru; Mohammadi, F.; Baleanu, Dumitru; 56389
The aim of the present study is to present a numerical algorithm for solving time-delay fractional optimal control problems (TDFOCPs). First, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet functions and their properties are implemented to derive some operational matrices. Then, the fractional derivative of the state function in the dynamic constraint of TDFOCPs is approximated by means of the Chelyshkov wavelets. The operational matrix of fractional integration together with the dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the performance index and necessary conditions for optimality transform the under consideration TDFOCPs into an algebraic system. Moreover, some illustrative examples are considered and the obtained numerical results were compared with those previously published in the literature.
A discussion on a generalized Geraghty multi-valued mappings and applications
(2020) Karapınar, Erdal; Atapour, Maryam; Karapınar, Erdal; 19184
This research intends to investigate the existence results for both coincidence points and common fixed point of generalized Geraghty multi-valued mappings endowed with a directed graph. The proven results are supported by an example. We also consider fractional integral equations as an application.
A Discussion on p-Geraghty Contraction on mw-Quasi-Metric Spaces
(2020) Karapınar, Erdal; Fulga, Andreea; Karapınar, Erdal; Tirado, Pedro; 19184
In this paper we consider a kind of Geraghty contractions by using mw-distances in the setting of complete quasi-metric spaces. We provide fixed point theorems for this type of mappings and illustrate with some examples the results obtained.
A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes
(2021) Baleanu, Dumitru; Mustafa, Ghulam; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In this article, we present the continuity analysis of the 3D models produced by the tensor product scheme of (m + 1)-point binary refinement scheme. We use differences and divided differences of the bivariate refinement scheme to analyze its smoothness. The C-0, C(1 )and C-2 continuity of the general bivariate scheme is analyzed in our approach. This gives us some simple conditions in the form of arithmetic expressions and inequalities. These conditions require the mask and the complexity of the given refinement scheme to analyze its smoothness. Moreover, we perform several experiments by using these conditions on established schemes to verify the correctness of our approach. These experiments show that our results are easy to implement and are applicable for both interpolatory and approximating types of the schemes.
A Drone-Based Blood Donation Approach Using an Ant Colony Optimization Algorithm
(2023) Jarad, Fahd; Ashraf, Faraha; Jarad, Fahd; Sardar, Muhammad Shoaib; Siddique, Imran; 234808
This article presents an optimized approach of mathematical techniques in the medical domain by manoeuvring the phenomenon of ant colony optimization algorithm (also known as ACO). A complete graph of blood banks and a path that covers all the blood banks without repeating any link is required by applying the Travelling Salesman Problem (often TSP). The wide use promises to accelerate and offers the opportunity to cultivate health care, particularly in remote or unmerited environments by shrinking lab testing reversal times, empowering just-in-time lifesaving medical supply.
A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures
(2023) Jarad, Fahd; Yusuf, Abdullahi; Tariboon, Jessada; Muhammad, Mubarak; Jarad, Fahd; Mikailu, Badamasi Bashir; 234808
The recurrence of outbreaks in cases of Ebola virus among African countries remains one of the greatest issues of concern. Practices such as hunting or consumption of contam-inated bush meat, unsafe funeral practices, and environmental contamination have all been implicated as possible contributors. This paper investigates the transmission dynamics of the Ebola virus model in the setting of a Caputo fractional-order derivative that accounts for both direct and indirect transmissions of the virus. By employing the concept of fixed theorems, we derived the existence and uniqueness results of the model. Moreover, we analyzed the forward normalized sensitivity indices to identify the critical parameters for controlling the infection and found that reducing the contact rate between infected individuals and susceptible vectors is vital to limiting the virus’s spread. Comparing the proposed fractional-order model with those of the previously developed integer-order model numerically, we found that the proposed model provides more reliable information on the model’s dynamics. Thus, we conclude that the Caputo fractional-order operator is a precise tool for describing the proposed model behavior and can help understand the complexities of Ebola virus disease outbreaks. © 2023, Thammasat University. All rights reserved.
A finite difference scheme to solve a fractional order epidemic model of computer virus
(2023) Iqbal, Zafar; Rehman, Muhammad Aziz-ur; Imran, Muhammad; Ahmed, Nauman; Fatima, Umbreen; Akgul, Ali; Rafiq, Muhammad; Raza, Ali; Djuraev, Ali Asrorovich; Jarad, Fahd
In this article, an analytical and numerical analysis of a computer virus epidemic model is presented. To more thoroughly examine the dynamics of the virus, the classical model is transformed into a fractional order model. The Caputo differential operator is applied to achieve this. The Jacobian approach is employed to investigate the model's stability. To investigate the model's numerical solution, a hybridized numerical scheme called the Grunwald Letnikov nonstandard finite difference (GL-NSFD) scheme is created. Some essential characteristics of the population model are scrutinized, including positivity boundedness and scheme stability. The aforementioned features are validated using test cases and computer simulations. The mathematical graphs are all detailed. It is also investigated how the fundamental reproduction number R0 functions in stability analysis and illness dynamics.
A Fixed Point Theorem and an Application for the Cauchy Problem in the Scale of Banach Spaces
(2020) Karapınar, Erdal; Karapınar, Erdal; 19184
The main aim of this paper is to prove the existence of the fixed point of the sum of two operators in setting of the cone-normed spaces with the values of cone-norm belonging to an ordered locally convex space. We apply this result to prove the existence of global solution of the Cauchy problem with perturbation of the form {x'(t) = f[t, x(t)] + g[t, x(t)], t is an element of[0,infinity), x(0) = x(0)is an element of F-1, in a scale of Banach spaces f(F-s; parallel to center dot parallel to(s)) : s is an element of(0, 1]}.
A fixed point theorem for a system of Pachpatte operator equations
(2021) Karapınar, Erdal; Öztürk, Ali; Rakocevic, Vladimir; 19184
In this paper, we investigate sufficient conditions for the existence of solutions to the system {Tx=x, alpha(i)(x)=0(E), i = 1,2, ... r, where 0(E) is the zero vector of E, and alpha(i) : E -> E i = 1, 2, ... , r are mappings, T is a mapping satisfying the Pachpatte-contraction.
A fixed point theorem without a Picard operator
(2021) Karapınar, Erdal; 19184
In this short note, we propose a fixed point theorem in the setting of a Banach space without using a Picard operator. © 2021, Cankaya University. All rights reserved.
A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations
(Global Science Press, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Zhao, Yue; 56389
A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the L-2 -norm are shown to be O(tau(2) + h(4)), where tau and h are time and space mesh sizes. Numerical examples confirm theoretical results.
A FRACTAL FRACTIONAL MODEL FOR CERVICAL CANCER DUE TO HUMAN PAPILLOMAVIRUS INFECTION
(2021) Baleanu, Dumitru; Ahmed, N.; Raza, A.; Iqbal, Z.; Rafiq, M.; Rehman, M. A.; Baleanu, Dumitru; 56389
In this paper, we have investigated women's malignant disease, cervical cancer, by constructing the compartmental model. An extended fractal-fractional model is used to study the disease dynamics. The points of equilibria are computed analytically and verified by numerical simulations. The key role of R-0 in describing the stability of the model is presented. The sensitivity analysis of R-0 for deciding the role of certain parameters altering the disease dynamics is carried out. The numerical simulations of the proposed numerical technique are demonstrated to test the claimed facts.
A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana-Baleanu fractional derivatives
(Pergamon-Elsevier Science LTD, 2018) Baleanu, Dumitru; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
The model of transmission dynamics of vector-borne diseases with vertical transmission and cure within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced. The effect of vertical transmission and cure rate on the basic reproduction number is shown. The Atangana-Baleanu fractional operator in caputo sense (ABC) with non-singular and non-local kernels is used to study the model. The existence and uniqueness of solutions are investigated using the Picard-Lindel method. Ultimately, for illustrating the acquired results, we perform some numerical simulations and show graphically to observe the impact of the arbitrary order derivative. It is expected that the proposed model will show better approximation than the classical model established before. (C) 2018 Elsevier Ltd. All rights reserved.

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Browsing Matematik Bölümü Yayın Koleksiyonu by Department "Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü"