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Öğe Mathematical analysis and pattern formation in diffusive predator–prey system(Springer Science and Business Media LLC, 2025-01-07) Nauman Ahmed; Muhammad Waqas Yasin; Ali Akgül; Dumitru Baleanu; Ovidiu Tintareanu-MirceaPrey-predator interactions are modeled using various dynamical systems and these interactions are affected by several factors. The predation rate of prey, reproduction rate, and prey use various strategies to avoid predation, the movement of the prey and predator species, food, and secured shelter can lead to the emergence of various types of patterns. These patterns in the prey-predator dynamics explain the complicated ecosystem. A reaction-diffusion prey-predator model with harvesting in predator is numerically investigated. A conditionally positivity preserving scheme is used. The von Neumann technique is used for the stability analysis. The Taylor series is used for the consistency analysis and discrete approximation is consistent with the underlying model. Pattern formation is observed for the governing model. The spot, stripe, and spot-stripes patterns are successfully gained that describe the complicated dynamics of the prey-predator dynamics. 3D and 2D simulations are drawn for the underlying model. The underlying model has two equilibria, both are successfully gained. All the theoretical results are verified through the simulations.Öğe Modeling and analysis of dengue transmission in fuzzy-fractional framework: a hybrid residual power series approach(Springer Science and Business Media LLC, 2024-12-28) Mubashir Qayyum; Qursam Fatima; Ali Akgül; Murad Khan HassaniThe current manuscript presents a mathematical model of dengue fever transmission with an asymptomatic compartment to capture infection dynamics in the presence of uncertainty. The model is fuzzified using triangular fuzzy numbers (TFNs) approach. The obtained fuzzy-fractional dengue model is then solved and analyzed through fuzzy extension of modified residual power series algorithm, which utilizes residual power series along with Laplace transform. Numerical analysis has also been performed in this study and obtained results are shown as solutions and residual errors for each compartment to ensure the validity. Graphical analysis depict the model’s behavior under varying parameters, illustrating contrasting trends for different values of and examining the impacts of transmission and recovery rates on dengue model in uncertain environment. The current findings highlighted the effectiveness of proposed uncertainty in epidemic system dynamics, offering new insights with potential applications in other areas of engineering, science and medicine.Öğe Computational analysis of Yamada–Ota and Xue models for surface tension gradient impact on radiative 3D flow of trihybrid nanofluid with Soret–Dufour effects(Springer Science and Business Media LLC, 2024-12-23) Sayer Obaid Alharbi; Munawar Abbas; Ahmed Babeker Elhag; Abdullah A. Faqihi; Ali AkgülThis article discusses the significance of Soret and Dufour, non-uniform heat generation, activation energy on radiative 3D flow of trihybrid nanofluid over a sheet with Marangoni convection. The energy equation takes into consideration the impacts of the heat generation, while the concentration equation takes activation energy into account. This trihybrid nanofluid is based on ethylene glycol and contains nanoparticles of titanium dioxide (TiO2), cobalt ferrite (CoFe2O), and aluminum oxide (Al2O3). For the case of trihybrid nanoparticles, the Yamada–Ota and Xue nanofluid models have been modified. This model is helpful for optimizing heating and cooling systems in fields like energy systems, microelectronics, and aerospace engineering where exact control of thermal properties is essential. By adjusting the characteristics of nanofluids, it also enhances heat transfer rates, which is a critical component in the development of solar collectors and high-efficiency heat exchangers. By using the necessary similarity transformations, non-linear ODEs are obtained from the controlling PDEs. The shooting method (BVP4c) can be utilized to solve this system of highly nonlinear equations numerically. As the surface tension gradient parameter is increased, the velocity distribution, mass transfer, and heat transfer rates all increase but the performance of the thermal and solutal profiles is opposite.Öğe Comparison study of modified and classical Hamilton-Crosser models for electrophoretic and thermophoretic particle deposition in stagnation point flow of diamond -SiC-Co3O4/diathermic oil-based trihybrid nanofluid(Springer, 2024) Ahmed M. Galal; Sahar Ahmed Idris; Munawar Abbas; Shaxnoza Saydaxmetova; Ali Hasan Ali; Humaira Kanwal; Ali AkgülThe current work examines the impact of heat generation on the stagnation point flow of a magnetized trihybrid nanofluid around a rotating sphere with electrophoretic and thermophoretic particle deposition. The trihybrid (Diamond –SiC–Co3O4/Do) nanofluid flow model consists of nanoparticles of Cobalt oxide (Co3O4), diamond (ND), and silicon carbide (SiC) dissolved in diathermic oil (DO). By comparing the modified model with the classical Hamilton–Crosser model, this study aims to investigate the heat transfer rate of a trihybrid nanofluid based on diamond –SiC–Co3O4/ diathermic oil. Through the analysis of trihybrid nanofluids based on diamond –SiC–Co3O4/Do diathermic oil, this model can optimize heat transmission in systems that need effective thermal management, like chemical reactors, electronics cooling, and energy storage. Trihybrid nanofluids' special qualities improve thermal conductivity, stability, and deposition control, which raises operational efficiency and dependability. It also helps with the design of sophisticated cooling systems for automotive and aerospace applications. These governing equations were solved with MATLAB's bvp4c tool after being transformed into ordinary differential equations via similarity variables. Results imply that, when compared to the classical model, the modified model accurately predicts higher heat transfer rates. As a consequence, trihybrid nanofluid heat transfer properties are better understood and thermal conductivity models are more accurate. The study shows that the concentration profile improved for both classical and modified Hamilton–Crosser models to enhance the values of electrophoretic particle deposition; while, inverse behavior is observed for thermophoretic particle deposition.Öğe Scrutinization of local thermal non-equilibrium effects on stagnation point flow of hybrid nanofluid containing gyrotactic microorganisms: a bio-fuel cells and bio-microsystem technology application(Springer, 2024) Okasha, Mostafa Mohamed; Abbas, Munawar; Formanova, Shoira; Faiz, Zeshan; Ali, Ali Hasan; Akgül, Ali; Galal, Ahmed M.The impact of Stefan blowing on the stagnation point flow of HNF (hybrid nanofluid) across a sheet containing gyrotactic microorganisms under local thermal non-equilibrium conditions (LTNECs) is briefly discussed in this paper. The present work uses a simplified mathematical model to inspect the characteristics of heat transfer in the absence of LTNECs (local thermal equilibrium conditions). LTNECs, traditionally provide two distinct fundamental temperature gradients for the liquid and solid phases simultaneously. A hybrid nanofluid is a mixture of water as the base fluid and single-walled carbon nanotubes and multi-walled carbon nanotubes. Gyrotactic microorganisms are included into nanoparticles to increase their thermal efficiency in a variety of systems, including microbial fuel cells, enzyme biosensors, bacteria powered micromixers, chip-shaped microdevices like bio-microsystems, and micro-volumes like microfluidic devices. This model can also help environmental engineering by enhancing wastewater treatment procedures by allowing microorganisms to break down pollutants more effectively. It advances the development of more productive photo bioreactors, increasing the output of biofuels in the field of renewable energy. Material scientists can utilize this concept to develop controlled nanostructured materials with consistent composition and thermal properties. The considerable similarity transformation is used to build ordinary differential equations for the nonlinear dimensionless system. This problem is solved numerically by using the Bvp4c method. The results determine that when the Stefan blowing parameter increases, fluid flow increases but temperature, mass transfer rate, and heat transfer are decreased.Öğe Öğe Öğe Öğe Delta(m)(p) Statistical Convergence of Order alpha(2018) Karakas, Abdulkadir; Altin, Yavuz; Et, MikailIn this work, we generalize the concepts of statistically convergent sequence of order alpha and statistical Cauchy sequence of order alpha by using the generalized difference operator Delta(m). We prove that a sequence is Delta(m)(p)-statistically convergent of order alpha if and only if it is Delta(m)(p)-statistically Cauchy of order alpha.Öğe On generalized statistical convergence of order β of sequences of fuzzy numbers(2014) A. Karakaş, Y. Altın, H. AltinokIn this article we introduce the concepts of Delta(m)(lambda)-statistical convergence of order beta and strong Delta(m)(lambda p)-summability of order beta for sequences of fuzzy numbers. Also, we establish some relations between the Delta(m)(lambda)-statistical convergence of order beta and strong Delta(m)(lambda p)-summability of order beta and we define w(lambda)(beta) (Delta(m), F, f, p), where f is a modulus function and give some inclusion relations.Öğe Almost statistical convergence of order of sequences of fuzzy numbers(2016) Karakas, Abdulkadir; Altin, Yavuz; Altinok, HifsiIn this article, we introduce the concepts of almost -statistical convergence of order and strongly almost -summability of order for sequences of fuzzy numbers. Also, we establish some relations between the almost -statistical convergence of order and strongly almost -summability of order and we define , where is a modulus function and give some inclusion relations.Öğe Actions of Soft Groups(International Conference on Applied Analysis and Mathematical Modeling, 2017) Oguz, Gulay…Öğe The Equivalence of Soft Group-Groupoids and Soft Crossed Modules(International Conference on Computational Mathematics and Engineering Sciences, 2018) Oguz, Gulay…Öğe Öğe ON LACUNARY STATISTICAL BOUNDEDNESS OF ORDER ALPHA(FACTA UNIVERSITATIS (NIˇS) Ser. Math. Inform., 2016) ET, Mikail; Mohiuddine, Syed A.; Şengül, HacerThe aim of this paper is to introduce and examine the concept of lacunary statistical boundedness of order and give the relations between statistical boundedness and lacunary statistical boundedness of order.Öğe Some basic inequalities for submanifolds of nearly quasi-constant curvature manifolds(Differential Geometry and Dinamical Systems, 2014) Gülbahar, Mehmet; Kılıç, Erol; Keleş, Sadık; Tripathi, Mukut ManiCertain basic inequalities involving the squared mean curvature and one of the Ricci curvature, the scalar curvature and the sectional curvature for a submanifold of quasi-constant curvature manifolds and nearly quasi-constant curvature manifolds are obtained. Equality cases are also discussed.Öğe Special proper pointwise slant surfaces of a locally product Riemannian manifold(Turkish Journal of Mathematics, 2015) Gülbahar, Mehmet; Kılıç, Erol; Saraçoğlu Çelik, SemraThe structure of pointwise slant submanifolds in an almost product Riemannian manifold is investigated and the special proper pointwise slant surfaces of a locally product manifold are introduced. A relation involving the squared mean curvature and the Gauss curvature of pointwise slant surface of a locally product manifold is proved. Two examples of proper pointwise slant surfaces of a locally product manifold, one of which is special and the other one is not special, are given.Öğe A USEFUL ORTHONORMAL BASIS ON BI-SLANT SUBMANIFOLDS OF ALMOST HERMITIAN MANIFOLDS(Tamkang Journal of Mathematics, 2016) Gülbahar, Mehmet; Kılıç, Erol; Keleş, SadıkIn this paper, we study bi-slant submanifolds of an almost Hermitian manifold for different cases. We introduce a new orthonormal basis on bi-slant submanifold, semi-slant submanifold and hemi-slant submanifold of an almost Hermitian manifold to compute Chen’s main inequalities. We investigate these inequalities for semi-slant submanifolds, hemi-slant submanifolds and slant submanifolds of a generalized complex space form. We obtain some characterizations on such submanifolds of a complex space form.Öğe On the sectional curvature of lightlike submanifolds(Journal of Inequalities and Applications, 2016) Kılıç, ErolThe main purpose of this paper is to show how to obtain rigidity theorems with the help of curvature invariants in submanifolds of a semi-Riemannian manifold. For this purpose, the bounded sectional curvature is introduced and some special submanifolds of r-lightlike submanifolds of a semi-Riemannian manifold are investigated.
