Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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: 1Unveiling the Strain Uniformity Challenge: Design and Evaluation of a Pdms Membrane for Precise Mechanobiology Studies(Taylor & Francis Ltd, 2025) Duz, Nilufer; Gulsum, Yasin; Odeibat, Waleed; Uyanik, Ismail; Akar, Samet; Dincer, PervinMechanotransduction and mechanosensing enable cells to respond to mechanical stimuli, essential in various physiological functions. Specialized cell stretching devices use stretchable, transparent, and biocompatible elastomeric membranes to study these responses. However, achieving strain uniformity is a key challenge, affecting data accuracy and reliability. This study designed a polydimethylsiloxane (PDMS) membrane with optimized uniformity for electromechanical cell stretching. Finite element analysis optimized membrane size and shape, achieving a 90% strain uniformity index-a 233% improvement over commercial membranes. By tailoring material properties like cross-linker ratio and curing time, membrane failure issues were resolved, enhancing applications in tissue engineering and mechanobiology research.Article Citation - WoS: 4Citation - Scopus: 4Microstructure and Mechanical Properties of Al-Co High Entropy Alloys(Taylor & Francis Ltd, 2022) Ayrenk, A.; Kalay, IThe structure and mechanical properties of non-equiatomic Al8Co30Cr18Fe9Ni31Nb4, Al8Co30Cr18Fe9Ni31Nb2Ti2 and Al8Co30Cr18Fe9Ni31Ti4 high entropy alloys (HEAs) were investigated using X-ray diffraction (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM), hardness and tensile testing. TEM and XRD analyses revealed the formation of gamma''-Ni3Nb/gamma (FCC), double FCC and gamma'-Ni3Al/gamma (FCC) structure for as-cast Al8Co30Cr18Fe9Ni31Nb4, Al8Co30Cr18Fe9Ni31Nb2Ti2 and Al8Co30Cr18Fe9Ni31Ti4 HEAs, respectively. The hardness and yield strength values were found to increase with the addition of Nb while the ductility of alloys increased with the increase in Ti concentration, significantly. The as-cast Al8Co30Cr18Fe9Ni31Ti4 alloy exhibited an excellent combination of ultimate tensile strength of 844 MPa and an elongation of 29.8% due to the coherent phase relation between gamma' precipitates and gamma matrix. The fractured surfaces of as-cast Al8Co30Cr18Fe9Ni31Nb4, Al8Co30Cr18Fe9Ni31Nb2Ti2 and Al8Co30Cr18Fe9Ni31Ti4 HEAs showed typical dimple type ductile fracture under tension test.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: 4Laser Array Field Correlations in Underwater Turbulence(Taylor & Francis Ltd, 2022) Gokce, Muhsin C.; Baykal, Yahya; Ata, YalcinIn underwater turbulent medium, field correlations are found when the incidence is a laser beam array. Variations of the field correlations against the variations in the ring radius of laser array beam, number of beamlets composing the laser array, source size, underwater turbulence parameters, i.e. the ratio of temperature to salinity contributions to the refractive index spectrum, rate of dissipation of mean-squared temperature and rate of dissipation of kinetic energy per unit mass of fluid, are investigated. Field correlations of laser arrays are found to be larger than the field correlations of the single beams. The effect of underwater turbulence is to reduce the field correlation of laser arrays.Article Citation - WoS: 6Citation - Scopus: 9Applications of the Novel Diamond Alpha Hardy-Copson Type Dynamic Inequalities To Half Linear Difference Equations(Taylor & Francis Ltd, 2022) Kaymakcalan, Billur; Kayar, ZeynepThis paper is devoted to novel diamond alpha Hardy-Copson type dynamic inequalities, which are zeta < 0 complements of the classical ones obtained fort zeta > 1, and their applications to difference equations. We obtain two kinds of diamond alpha Hardy-Copson type inequalities for zeta < 0, one of which is mixed type and established by the convex linear combinations of the related delta and nabla inequalities while the other one is new and is obtained by using time scale calculus rather than algebra. In contrast to the works existing in the literature, these complements are derived by preserving the directions of the classical inequalities. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities obtained for zeta < 0 into one diamond alpha Hardy-Copson type inequalities and offer new types of diamond alpha Hardy-Copson type inequalities which have the same directions as the classical ones and can be considered as complementary inequalities. Moreover the application of these inequalities in the oscillation theory of half linear difference equations provides several nonoscillation criteria for such equations.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: 3Citation - Scopus: 4Po and Ptd Approach To the Diffraction Problem by a Resistive Half-Plane(Taylor & Francis Ltd, 2014) Basdemir, Husnu DenizDiffracted fields from a resistive half-plane were investigated by the method of physical optics (PO) and the physical theory of diffraction. The coefficient of the PO scattering integral was derived for the first time for the resistive half-plane. Uniform fringe field expressions were obtained in terms of the Fresnel functions. The resultant expressions of the fringe fields were plotted and analyzed numerically.