WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - Scopus: 1Finite Bivariate Biorthogonal N - Konhauser Polynomials(Taylor & Francis Ltd, 2025) Lekesiz, E. Guldogan; Cekim, B.; Ozarslan, M. A.; Güldoğan Lekesiz, E.A new set of finite 2D biorthogonal polynomials is defined using the finite orthogonal polynomials $ N_{n}<^>{\left (p\right ) }\left (w\right ) $ Nn(p)(w) and Konhauser polynomials. We present a connection between this finite 2D biorthogonal set and the generalized Laguerre-Konhauser polynomials. Also, we obtain several applications of finite bivariate biorthogonal N - Konhauser polynomials.Article Citation - WoS: 11Citation - Scopus: 18Analysis of the family of integral equation involving incomplete types of I and Ī-functions(Taylor & Francis Ltd, 2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil DuttThe present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.Article Citation - WoS: 5Citation - Scopus: 6Convoluted Fractional Differentials of Various Forms Utilizing the Generalized Raina's Function Description With Applications(Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Ibrahim, Rabha W.A generalized differential operator utilizing Raina's function is constructed in light of a certain type of fractional calculus. We next use the generalized operators to build a formula for analytic functions of type normalized. Our method is based on the concepts of subordination and superordination. As an application, a class of differential equations involving the suggested operator is studied. As seen, the solution is provided by a certain hypergeometric function. We also create a fractional coefficient differential operator. Its geometric and analytic features are discussed. Finally, we use the Jackson's calculus to expand the Raina's differential operator and investigate its properties in relation to geometric function theory.Article Citation - WoS: 18Citation - Scopus: 20Comprehending the Model of Omicron Variant Using Fractional Derivatives(Taylor & Francis Ltd, 2023) Goswami, Pranay; Baleanu, Dumitru; Shankar Dubey, Ravi; Sharma, ShivaniThe world is grappled with an unprecedented challenges due to Corona virus. We are all battling this epidemic together, but we have not been able to defeat this epidemic yet. A new variant of this virus, named 'Omicron' is spreading these days. The fractional differential equations are providing us with better tools to study the mathematical model with memory effects. In this paper, we will consider an extended SER mathematical model with quarantined and vaccinated compartment to speculate the Omicron variant. This extended Susceptible Exposed Infected Recovered SER model involves equations that associate with the group of individuals those are susceptible (S), exposed (E): this class includes the individuals who are infected but not yet infectious, infectious (W): this class includes the individuals who are infected but not yet Quarantined, quarantined (Q): this class includes those group of people who are infectious, confirmed and quarantined, recovered (R) this class includes the group of individuals who have recovered, and vaccinated (V): this class includes the group of individuals who have been vaccinated. The non-negativity and of the extended SER model is analysed, the equilibrium points and the basic reproduction number are also calculated. The proposed model is then extended to the mathematical model using AB derivative operator. Proof for the existence and the uniqueness for the solution of fractional mathematical model in sense of AB fractional derivative is detailed and a numerical method is detailed to obtain the numerical solutions. Further we have discussed the efficiency of the vaccine against the Omicron variant via graphical representation.Article Citation - WoS: 11Citation - Scopus: 18Analysis of the Family of Integral Equation Involving Incomplete Types of I and (i)over-Bar(Taylor & Francis Ltd, 2023) Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D. L.; Purohit, Sunil Dutt; Bhatter, SanjayThe present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (I/F) and an incomplete (I) over bar -function ((I/F) over bar) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (I) over bar -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.Article Citation - WoS: 13Citation - Scopus: 16A Generalized Study of the Distribution of Buffer Over Calcium on a Fractional Dimension(Taylor & Francis Ltd, 2023) Jangid, Kamlesh; Kumawat, Shyamsunder; Purohit, Sunil Dutt; Baleanu, Dumitru; Suthar, D. L.; Bhatter, SanjayCalcium is an essential element in our body and plays a vital role in moderating calcium signalling. Calcium is also called the second messenger. Calcium signalling depends on cytosolic calcium concentration. In this study, we focus on cellular calcium fluctuations with different buffers, including calcium-binding buffers, using the Hilfer fractional advection-diffusion equation for cellular calcium. Limits and start conditions are also set. By combining with intracellular free calcium ions, buffers reduce the cytosolic calcium concentration. The buffer depletes cellular calcium and protects against toxicity. Association, dissociation, diffusion, and buffer concentration are modelled. The solution of the Hilfer fractional calcium model is achieved through utilizing the integral transform technique. To investigate the influence of the buffer on the calcium concentration distribution, simulations are done in MATLAB 21. The results show that the modified calcium model is a function of time, position, and the Hilfer fractional derivative. Thus the modified Hilfer calcium model provides a richer physical explanation than the classical calcium model.Article Citation - WoS: 15Citation - Scopus: 15A Constraint Programming Approach To a Real-World Workforce Scheduling Problem for Multi-Manned Assembly Lines With Sequence-Dependent Setup Times(Taylor & Francis Ltd, 2024) Kandiller, Levent; Drake, John H.; Guner, Funda; Gorur, Abdul K.; Satir, BenhurFor over five decades, researchers have presented various assembly line problems. Recently, assembly lines with multiple workers at each workstation have become very common in the literature. These lines are often found in the manufacturing of large vehicles, where workers at a workstation may perform their assigned tasks at the same time. Most research on multi-manned assembly lines focuses on balancing tasks and workers among workstations and scheduling tasks for workers. This study, however, concentrates on assigning tasks to workers already assigned to a specific workstation, rather than balancing the entire line. The problem was identified through an industrial case study at a large vehicle manufacturing company. The study presents two methods, one using mixed integer linear programming and the other using constraint programming, to minimise the number of workers required on a multi-manned assembly line with sequence-dependent setup times. The results of the computational experiments indicate that the constraint programming method performs better than the mixed integer linear programming method on several modified benchmark instances from the literature. The constraint programming model is also tested on the real-world scenario of our industrial case study and leads to significant improvements in the productivity of the workstations.Article Citation - WoS: 3Citation - Scopus: 3On the Fixed Points of Iterative Contractive Mappings Defined Via Implicit Relation(Taylor & Francis Ltd, 2021) Erhan, Inci M.; Fulga, Andreea; Karapinar, Erdal; Aksoy, UmitIn this paper, we consider an implicit relation to generalize iterative fixed point results in the literature in the context of metric spaces. We conclude that several existing results are immediate consequences of our main results.Article Citation - WoS: 56Citation - Scopus: 59Nonlinear Generalized Fractional Differential Equations With Generalized Fractional Integral Conditions(Taylor & Francis Ltd, 2020) Ravichandran, Chokkalingam; Jarad, Fahd; Belmor, SamihaThis research work is dedicated to an investigation of the existence and uniqueness of a class of nonlinear psi-Caputo fractional differential equation on a finite interval , equipped with nonlinear psi-Riemann-Liouville fractional integral boundary conditions of different orders , we deal with a recently introduced psi-Caputo fractional derivative of order . The formulated problem will be transformed into an integral equation with the help of Green function. A full analysis of existence and uniqueness of solutions is proved using fixed point theorems: Leray-Schauder nonlinear alternative, Krasnoselskii and Schauder's fixed point theorems, Banach's and Boyd-Wong's contraction principles. We show that this class generalizes several other existing classes of fractional-order differential equations, and therefore the freedom of choice of the standard fractional operator. As an application, we provide an example to demonstrate the validity of our results.Article Citation - WoS: 4Citation - Scopus: 4Hegemonic Masculinity and Terrorism: the Case of the Pkk and Abdullah Ocalan(Taylor & Francis Ltd, 2020) Turk, H. Bahadir; Bahadır Türk, H.Recent years have seen an increase in the study of the relationship between gender and terrorism. This article analyzes the relationship between hegemonic masculinity and terrorism through the case of the Kurdistan Workers' Party (Partiya Karkeren Kurdistan or PKK) and its leader Abdullah ocalan. Using the method of narrative analysis, the study first examines the concept of hegemonic masculinity. The study attempts to make sense of how the concept of hegemonic masculinity operates within the PKK. To achieve this goal, the study demonstrates the major functions of hegemonic masculinity within terrorist organisations. Accordingly, it is argued that the perspective of masculinity studies can be used to gain a better and highly instructive understanding of political violence and terrorism.