Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 2Citation - Scopus: 7A Necessary and Sufficient Condition for Oscillation of Second Order Sublinear Delay Dynamic Equations(Amer inst Mathematical Sciences-aims, 2011) Mert, RazIye; Mert, Raziye; Zafer, Agacik; MatematikTime scale calculus approach allows one to treat the continuous, discrete, as well as more general systems simultaneously. In this article we use this tool to establish a necessary and sufficient condition for the oscillation of a class of second order sublinear delay dynamic equations on time scales. Some well known results in the literature are improved and extended.Article Citation - WoS: 23Citation - Scopus: 23Ostrowski Type Inequalities Via New Fractional Conformable Integrals(Amer inst Mathematical Sciences-aims, 2019) Set, Erhan; Akdemir, Ahmet Ocak; Gozpinar, Abdurrahman; Jarad, Fahd; Rashid, Saima; Safdar, Farhat; Noor, Muhammad Aslam; Noor, Khalida InayatIn this present study, firstly, some necessary definitions and some results related to Riemann-Liouville fractional and new fractional conformable integral operators defined by Jarad et al. [13] are given. As a second, a new identity has been proved. By using this identity, new Ostrowski type inequalities has obtained involving fractional conformable integral operators. Also, some new inequalities has established for AG-convex functions via fractional conformable integrals in this study. Relevant connections of the results presented here with those earlier ones are also pointed out.Article Citation - WoS: 1Citation - Scopus: 3Hopf Bifurcations of a Lengyel-Epstein Model Involving Two Discrete Time Delays(Amer inst Mathematical Sciences-aims, 2022) Bilazeroglu, Seyma; Merdan, Huseyin; Guerrini, LucaHopf bifurcations of a Lengyel-Epstein model involving two discrete time delays are investigated. First, stability analysis of the model is given, and then the conditions on parameters at which the system has a Hopf bifurcation are determined. Second, bifurcation analysis is given by taking one of delay parameters as a bifurcation parameter while fixing the other in its stability interval to show the existence of Hopf bifurcations. The normal form theory and the center manifold reduction for functional differential equations have been utilized to determine some properties of the Hopf bifurcation including the direction and stability of bifurcating periodic solution. Finally, numerical simulations are performed to support theoretical results. Analytical results together with numerics present that time delay has a crucial role on the dynamical behavior of Chlorine Dioxide-Iodine-Malonic Acid (CIMA) reaction governed by a system of nonlinear differential equations. Delay causes oscillations in the reaction system. These results are compatible with those observed experimentally.Article Citation - WoS: 14Citation - Scopus: 16Analysis of the Fractional Diarrhea Model With Mittag-Leffler Kernel(Amer inst Mathematical Sciences-aims, 2022) Iqbal, Muhammad Sajid; Ahmed, Nauman; Akgul, Ali; Raza, Ali; Shahzad, Muhammad; Iqbal, Zafar; Jarad, FahdIn this article, we have introduced the diarrhea disease dynamics in a varying population. For this purpose, a classical model of the viral disease is converted into the fractional-order model by using Atangana-Baleanu fractional-order derivatives in the Caputo sense. The existence and uniqueness of the solutions are investigated by using the contraction mapping principle. Two types of equilibrium points i.e., disease-free and endemic equilibrium are also worked out. The important parameters and the basic reproduction number are also described. Some standard results are established to prove that the disease-free equilibrium state is locally and globally asymptotically stable for the underlying continuous system. It is also shown that the system is locally asymptotically stable at the endemic equilibrium point. The current model is solved by the Mittag-Leffler kernel. The study is closed with constraints on the basic reproduction number R-0 and some concluding remarks.Article Citation - WoS: 30Citation - Scopus: 33Dynamics of Fractional Order Delay Model of Coronavirus Disease(Amer inst Mathematical Sciences-aims, 2022) Zhang, Lei; Rahman, Mati Ur; Ahmad, Shabir; Riaz, Muhammad Bilal; Jarad, FahdThe majority of infectious illnesses, such as HIV/AIDS, Hepatitis, and coronavirus (2019-nCov), are extremely dangerous. Due to the trial version of the vaccine and different forms of 2019-nCov like beta, gamma, delta throughout the world, still, there is no control on the transmission of coronavirus. Delay factors such as social distance, quarantine, immigration limitations, holiday extensions, hospitalizations, and isolation are being utilized as essential strategies to manage the outbreak of 2019-nCov. The effect of time delay on coronavirus disease transmission is explored using a non-linear fractional order in the Caputo sense in this paper. The existence theory of the model is investigated to ensure that it has at least one and unique solution. The Ulam-Hyres (UH) stability of the considered model is demonstrated to illustrate that the stated model's solution is stable. To determine the approximate solution of the suggested model, an efficient and reliable numerical approach (Adams-Bashforth) is utilized. Simulations are used to visualize the numerical data in order to understand the behavior of the different classes of the investigated model. The effects of time delay on dynamics of coronavirus transmission are shown through numerical simulations via MATLAB-17.Article Citation - WoS: 6Citation - Scopus: 7Fixed Point Results of a New Family of Hybrid Contractions in Generalised Metric Space With Applications(Amer inst Mathematical Sciences-aims, 2022) Jiddah, Jamilu Abubakar; Noorwali, Maha; Shagari, Mohammed Shehu; Rashid, Saima; Jarad, FahdIn this manuscript, a novel general family of contraction, called hybrid-interpolative ReichIstrat,escu-type (G-alpha-mu)-contraction is introduced and some fixed point results in generalised metric space that are not deducible from their akin in metric spaces are obtained. The preeminence of this class of contraction is that its contractive inequality can be extended in a variety of manners, depending on the given parameters. Consequently, a number of corollaries that reduce our result to other wellknown results in the literature are highlighted and analysed. Substantial examples are constructed to validate the assumptions of our obtained theorems and to show their distinction from corresponding results. Additionally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution of a family of integral equations.Article Citation - WoS: 12Citation - Scopus: 20On the Decomposition and Analysis of Novel Simultaneous Seiqr Epidemic Model(Amer inst Mathematical Sciences-aims, 2023) Palanivelu, Balaganesan; Jayaraj, Renuka; Baleanu, Dumitru; Dhandapani, Prasantha Bharathi; Umapathy, KalpanaIn this manuscript, we are proposing a new kind of modified Susceptible Exposed Infected Quarantined Recovered model (SEIQR) with some assumed data. The novelty imposed here in the study is that we are studying simultaneously SIR, SEIR, SIQR, and SEQR pandemic models with the same data unchanged as the SEIQR model. We are taking this model a step ahead by using a non-helpful transition because it was mostly skipped in the literature. All sorts of features that are essential to study the models, such as basic reproduction number, stability analysis, and numerical simulations have been examined for this modified model with other models.Article Citation - WoS: 6Citation - Scopus: 7Fixed Point Results in C*-Algebra Bipolar Metric Spaces With an Application(Amer inst Mathematical Sciences-aims, 2023) Gnanaprakasam, Arul Joseph; Isik, Huseyin; Jarad, Fahd; Mani, GunaseelanIn this work, we prove existence and uniqueness fixed point theorems under Banach and Kannan type contractions on C*-algebra-valued bipolar metric spaces. To strengthen our main results, an appropriate example and an effective application are presented.Article Citation - WoS: 4Citation - Scopus: 6Existence and Ulam-Hyers Stability of Mild Solutions for Impulsive Integro-Differential Systems Via Resolvent Operators(Amer inst Mathematical Sciences-aims, 2025) Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, Erdal; Bensalem, AbdelhamidThe aim of this paper is to present existence, Ulam-Hyers-Rassias stability and continuous dependence on initial conditions for the mild solution of impulsive integro-differential systems via resolvent operators. Our analysis is based on fixed point theorem with generalized measures of noncompactness, this approach is combined with the technique that uses convergence to zero matrices in generalized Banach spaces. An example is presented to illustrate the efficiency of the result obtained.Article Citation - WoS: 5Citation - Scopus: 6An Inevitable Note on Bipolar Metric Spaces(Amer inst Mathematical Sciences-aims, 2024) Cvetkovic, Marija; Karapinar, ErdalBipolar metric spaces and related fixed point theorems therein were introduced based on the motivation of measuring the distance between the elements of distinct sets. The question regarding the independence of these results from the analogous results on a fixed point of an induced mapping on a Cartesian product of two sets. We proved that bipolar metric space is metrizable and we presented two different approaches for defining a metric induced by a bipolar metric. Two obtained metric spaces demonstrated the lack of novelty of fixed point theorems for covariant and contravariant contraction.