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: 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 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 Numerical investigation on the performance of a small scale solar chimney power plant for different geometrical parameters(Elsevier Sci Ltd, 2020) Özgirgin Yapıcı, Ekin; Nsaif, Osama; Aylı, Ece; Yapici, Ekin OzgirginIn recent decades, demand for energy has been significantly increased, and considering environmental impacts and the degrading nature of fossil fuels, clean and emission-free renewable energy production has attracted a great deal of attention. One of the most promising renewable energy sources is solar energy due to low cost and low harmful emissions, and from the 1980s, one of the most beneficial applications of solar energy is the utilization of solar chimney power plants (SCPP). A SCPP is a simple and reliable system that consists of three main components; a solar collector, a chimney (tower) and a turbine to utilize electrical energy. Recently, by the advancement in computer technology, the use of CFD methodology for studying SCPP has become an extensive, robust and powerful technique. In light of the above, in this study, numerical simulations of a SCPP through three-dimensional axisymmetric modeling is performed. A numerical model is created using CFD software, and the results are verified with an experimental study from the literature. After ensuring good agreement with the experiments, chimney's and collector's geometric parameters effects and different configurations effects on SCPP performance, simultaneously and additively is investigated. The study introduces an insight to the performance enhancement methods and finding the best configuration of a SCPP model, which will be the basis of a detailed prototyping process. Based on the numerical results, the best configuration of the SCPP has been found as the diverging chimney which enhances the generated power. The results of the study showed that the chimney height and collector radius increase has a positive effect on the power output and efficiency of the system, but when construction and material costs are also considered, each has an optimal value. The maximum impact on the performance is found to be by the chimney tower radius and the collector height and inclination are found to have optimum values considering performance. According to the obtained results, the best performance for the SCPP was obtained with 3.5 m chimney height, 30 cm tower diameter, 400 cm of collector diameter with 6 cm height and zero inclination angle. By the correct selection of the dominant performance parameter which can be done by correctly interpreting the results of this study, "the best" design of a SCPP real scale prototype considering maximum power requirement can be done. (C) 2020 Elsevier Ltd. All rights reserved.Article 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. © 2021Article Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations(Pergamon-Elsevier Science Ltd, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; Bleanu, DumitruWe establish the long-time asymptotic formula of solutions to the (1+α)-order fractional differential equation 0iOt1+αx+a(t)x=0, t>0, under some simple restrictions on the functional coefficient a(t), where 0iOt1+α is one of the fractional differential operators 0Dtα(x′), (0Dtαx)′= 0Dt1+αx and 0Dtα(tx′-x). Here, 0Dtα designates the Riemann-Liouville derivative of order α∈(0,1). The asymptotic formula reads as [b+O(1)] ·xsmall+c·xlarge as t→+∞ for given b, c∈R, where xsmall and xlarge represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation 0iOt1+αx=0, t>0Article Some fixed point results for TAC-type contractive mappings(Hindawi Publishing Corporation, 2016) Chandok, Sumit; Taş, Kenan; Ansari, Arslan Hojat; Hojat Ansari, ArslanWe prove some fixed point results for new type of contractive mappings using the notion of cyclic admissible mappings in the framework of metric spaces. Our results extend, generalize, and improve some well-known results from literature. Some examples are given to support our main results.