Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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 δ-β-Gabor integral operators for a space of locally integrable generalized functions(Springer, 2020) Al-Omari, Shrideh Khalaf; Baleanu, Dumitru; Nisar, Kottakkaran SooppyIn this article, we give a definition and discuss several properties of the δ-β-Gabor integral operator in a class of locally integrable Boehmians. We derive delta sequences, convolution products and establish a convolution theorem for the given δ-β-integral. By treating the delta sequences, we derive the necessary axioms to elevate the δ-β-Gabor integrable spaces of Boehmians. The said generalized δ-β-Gabor integral is, therefore, considered as a one-to-one and onto mapping continuous with respect to the usual convergence of the demonstrated spaces. In addition to certain obtained inversion formula, some consistency results are also given.Article The first observation of memory effects in the infrared (FT-IR) measurements: Do successive measurements remember each other?(Public Library Science, 2014) Nigmatullin, Raoul R.; Osokin, Sergey I.; Baleanu, Dumitru; Al-Amri, Sawsan; Azam, Ameer; Memic, AdnanOver the past couple of decades there have been major advances in the field of nanoscience and nanotechnology. Many applications have sprouted from these fields of research. It is essential, given the scale of the materials, to attain accurate, valid and reproducible measurements. Material properties have shown to be a function of their size and composition. Physiochemical properties of the nanomaterials can significantly alter material behavior compared to bulk counterparts. For example, metal oxide nanoparticles have found broad applications ranging from photo-catalysis to antibacterial agents. In our study, we synthesized CuO nanoparticles using well established sol-gel based methods with varying levels of Ni doping. However, upon analysis of measured infrared data, we discovered the presence of quasi-periodic (QP) processes. Such processes have previously been reported to be tightly associated with measurement memory effects. We were able to detect the desired QP process in these measurements from three highly accurate repetitive experiments performed on each Ni (1-7%) doped CuO sample. In other words, successive measurements performed in a rather short period of time remember each other at least inside a group of neighboring measurements.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 On fractional order hybrid differential equations(Hindawi Publishing Corporation, 2014) Herzallah, Mohamed A. E.; Baleanu, DumitruWe develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0 << 1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.Article On a new class of fractional operators(Springeropen, 2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, DumitruThis manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.Article Numerical Simulation of Mixed Convection Squeezing Flow of a Hybrid Nanofluid Containing Magnetized Ferroparticles in 50%:50% of Ethylene Glycol–Water Mixture Base Fluids Between Two Disks With the Presence of a Non-linear Thermal Radiation Heat Flux(Frontiers Media SA, 2020) Nisar, Kottakkaran Sooppy; Khan, Umair; Zaib, A.; Khan, Ilyas; Baleanu, DumitruFerroliquids are an example of a colloidal suspension of magnetic nanomaterials and regular liquids. These fluids have numerous applications in medical science such as cell separation, targeting of drugs, magnetic resonance imaging, etc. The hybrid nanofluid is composed by scattering the magnetic nanomaterial of more than one type nanoparticles suspended into the base fluid. It has different scientific applications such as heat dissipation, dynamic sealing, damping, etc. Owing to the vast ferrofluid applications, the time-dependent squeezed flow of hybrid ferroliquids under the impact of non-linear radiation and mixed convection within two disks was explored for the first time in this analysis. Here, the cobalt and magnetite ferrofluids are considered and scattered in a 50%:50% mixture of water–EG (ethylene glycol). The similarity technique is used to reduce the leading PDEs into coupled non-linear ODEs. The transmuted equations together with recommended boundary restrictions are numerically solved via Matlab solver bvp4c. The opposing and assisting flows are considered. The impacts of an emerging parameter on fluid velocity and temperature field of hybrid ferroliquids are examined through the different graphical aids. The results showed that the opposite trend is scrutinized due to the magnetic influence on the temperature and velocity in the case of assisting and opposing flows. The velocity augments due to the volume fraction of nanoparticles in the assisting flow and declines in the opposing flow, while the opposite direction is noticed in the temperature field. © Copyright © 2020 Nisar, Khan, Zaib, Khan and Baleanu.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 A k-Dimensional System of Fractional Finite Difference Equations(Hindawi Ltd, 2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, SaeidWe investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.