WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 3Citation - Scopus: 3Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme(Amer Inst Mathematical Sciences-AIMS, 2022) Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, KazemIn the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.Article Citation - WoS: 13Citation - Scopus: 17Nonautonomous lump-periodic and analytical solutions tothe (3+1)-dimensional generalized Kadomtsev-Petviashviliequation(Springer, 2023) Alquran, Marwan; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, DumitruThis work establishes the lump periodic and exact traveling wave solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation. We use the Hirota bilinear method, as well as the robust integration techniques tanh-coth expansion and rational sine-cosine, to provide such innovative solutions. In order to explain specific physical difficulties, innovative lump periodic and analytical solutions have been investigated. These discoveries have been proven to be useful in the transmission of long-wave and high-power communications networks. It is important to highlight that the results given in thiswork depict new features and reflect previously unknown physical dynamics for the governing model.Conference Object Citation - Scopus: 1Fractional Order Computing and Modeling with Portending Complex Fit Real-World Data(Springer International Publishing AG, 2023) Karaca, Yeliz; Rahman, Mati ur; Baleanu, DumitruFractional computing models identify the states of different systems with a focus on formulating fractional order compartment models through the consideration of differential equations based on the underlying stochastic processes. Thus, a systematic approach to address and ensure predictive accuracy allows that the model remains physically reasonable at all times, providing a convenient interpretation and feasible design regarding all the parameters of the model. Towards these manifolding processes, this study aims to introduce new concepts of fractional calculus that manifest crossover effects in dynamical models. Piecewise global fractional derivatives in sense of Caputo and Atangana-Baleanu-Caputo (ABC) have been utilized, and they are applied to formulate the Zika Virus (ZV) disease model. To have a predictive analysis of the behavior of the model, the domain is subsequently split into two subintervals and the piecewise behavior is investigated. Afterwards, the fixed point theory of Schauder and Banach is benefited from to prove the existence and uniqueness of at least one solution in both senses for the considered problem. As for the numerical simulations as per the data, Newton interpolation formula has been modified and extended for the considered nonlinear system. Finally, graphical presentations and illustrative examples based on the data for various compartments of the systems have been presented with respect to the applicable real-world data for different fractional orders. Based on the impact of fractional order reducing the abrupt changes, the results obtained from the study demonstrate and also validate that increasing the fractional order brings about a greater crossover effect, which is obvious from the observed data, which is critical for the effective management and control of abrupt changes like infectious diseases, viruses, among many more unexpected phenomena in chaotic, uncertain and transient circumstances.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 - Scopus: 1Remarks On Some Generalizations Of θ-Contraction(Univ Politehnica Bucharest, Sci Bull, 2023) Karapınar, Erdal; Cvetkovic, MarijaThe concept of θ-contraction was modified and generalized in several ways during the last decade. Some assumptions concerning the class Θ are shown to be super-fluous in order to obtain a unique fixed point for a θ-type contraction, θ-Suzuki type and, consequently, θ-contraction. Improvement of several previously published results are de-rived with a modified contractive condition and we have presented an example of possible application. The same approach was used for the F-Suzuki contraction and numerous generalizations are made.Article The analytical analysis of nonlinear fractional-order dynamical models(Amer Inst Mathematical Sciences-AIMS, 2021) Xu, Jiabin; Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, DumitruThe present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.Article Citation - Scopus: 32New extensions of Hermite–Hadamard inequalities via generalized proportional fractional integral(John Wiley and Sons Inc, 2021) Mumcu, İlker; Set, Erhan; Akdemir, Ahmet Ocak; Jarad, FahdThe main aim this work is to give Hermite–Hadamard inequalities for convex functions via generalized proportional fractional integrals. We also obtained extensions of Hermite–Hadamard type inequalities for generalized proportional fractional integrals. © 2021 Wiley Periodicals LLCArticle Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating(Elsevier, 2021) Aziz-Ur, Rehman; Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; Aziz-ur-rehman,The classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results. © 2021