Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 30Citation - Scopus: 31Heat and Mass Transport Impact on MHD Second-Grade Fluid: A Comparative Analysis of Fractional Operators(Wiley, 2021) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Akgul, Ali; Saeed, Syed Tauseef; Baleanu, DumitruThe effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in different fields, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of magnetohydrodynamic (MHD) unsteady second-grade fluid in the presence of ramped conditions. The new governing equations of MHD second-grade fluid have been fractionalized by means of singular and nonsingular differentiable operators. To have an accurate physical significance of imposed conditions on the geometry of second-grade fluid, the constant concentration with ramped temperature and ramped velocity is considered. The fractional solutions of temperature, concentration, and velocity have been investigated by means of integral transform and inversion algorithm. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect.Article Citation - WoS: 1Citation - Scopus: 2Testing the Equality of Several Independent Stationary and Non-Stationary Time Series Models with Fractional Brownian Motion Errors(Elsevier, 2021) Mahmoudi, Mohammad Reza; Baleanu, Dumitru; Qasem, Sultan Noman; Mosavi, Amirhosein; Band, Shahab S.; S. Band, ShahabThis work is devoted to apply the parametric and nonparametric techniques to construct test of hypothesis about the equality of the probabilistic behaviors of several time series models with fractional Brownian motion errors fitted on several independent datasets. The accuracy and power of the introduced method are studied using the simulated and real datasets. The results indicate that the introduced approach is more powerful than other alternative approaches, in non-stationary cases. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Article Citation - WoS: 180Citation - Scopus: 192On Fractional Calculus with General Analytic Kernels(Elsevier Science Inc, 2019) Fernandez, Arran; Ozarslan, Mehmet Ali; Baleanu, DumitruMany possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions. We demonstrate, under some assumptions, how all of these modifications can be considered as special cases of a single, unifying, model of fractional calculus. We provide a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann-Liouville fractional integral operator. We also consider inversion properties of the new operators, prove analogues of the Leibniz and chain rules in this model of fractional calculus, and solve some fractional differential equations using the new operators. (C) 2019 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3Existence Results for Block Matrix Operator of Fractional Orders in Banach Algebras(MDPI, 2019) Hashem, Hind; El-Sayed, Ahmed; Baleanu, DumitruThis paper is concerned with proving the existence of solutions for a coupled system of quadratic integral equations of fractional order in Banach algebras. This result is a direct application of a fixed point theorem of Banach algebras. Some particular cases, examples and remarks are illustrated. Finally, the stability of solutions for that coupled system are studied.Article Citation - WoS: 3Citation - Scopus: 2Surface Terms, Angular Momentum and Hamilton-Jacobi Formalism(Soc Italiana Fisica, 2003) Güler, Y; Baleanu, Dumitru; Baleanu, D; Cenk, M; MatematikQuadratic Lagrangians are introduced adding surface terms to a free-particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of a constrained system. The manifold structure induced by the quadratic Lagrangian is investigated.Article Citation - Scopus: 4On Mild Solution of Abstract Neutral Fractional Order Impulsive Differential Equations With Infinite Delay(Eudoxus Press, LLC, 2018) Anguraj, A.; Baleanu, Dumitru; Kanjanadevi, S.; Baleanu, D.; MatematikWe prove the existence and uniqueness of fractional neutral impulsive differential equations with infinite delay via contraction mapping principle and fixed point technique for condensing map. We use the resolvent operator technique for integral equations to make the mild solution of the problem more appropriate. © 2018 by Eudoxus Press, LLC. All rights reserved.Article Citation - WoS: 36Citation - Scopus: 41Numerical Treatment of Coupled Nonlinear Hyperbolic Klein-Gordon Equations(Editura Acad Romane, 2014) Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; Baleanu, D.; Abdelkawy, M. A.; MatematikA semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nystrom scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.Article Modelling the Latex Spreading on Clay(Chiminform Data S A, 2014) Al-Turaif, Hamad A.; Baleanu, Dumitru; Baleanu, Dumitru; MatematikIn this manuscript a model was proposed in order to predict the extent of the latex spreading on clay pigment. The results from Scan Electron Microscopy (SEM) and X-ray Photoelectron Spectroscopy (XPS) were used to evaluate the predicted results. A good agreement of the predicted results was found.Article Citation - WoS: 7On Dynamics of Fractional-Order Model of Hcv Infection(Univ Prishtines, 2017) Khodabakhshi, Neda; Baleanu, Dumitru; Vaezpour, S. Mansour; Baleanu, Dumitru; MatematikIn this paper, we investigate the dynamical behavior of the fractional-order model within Caputo derivative of HCV infection. Stability analysis of the equilibrium points is according to the basic reproduction number R-0. The numerical simulations are also presented to illustrate the results.Article Citation - WoS: 8Citation - Scopus: 8Determination of Salicin Content of Some Salix L. Species by Hplc Method(Chiminform Data S A, 2007) Guvenc, Aysegul; Baleanu, Dumitru; Arihan, Okan; Altun, M. Levent; Dinc, Erdal; Baleanu, Dumitru; MatematikIn this paper, we find the salicin content of the nine species of Salix L from the province of Ankara, Turkey, namely Salix triandra, S. alba, S. excelsa, S. fragilis, S. babylonica, S. caprea, S. cinerea, S. pseudomedemii and S. amplexicaulis. A simple HPLC method was applied to the determination of Salicin of these nine species in barks and leaves of female and male. Chromatographic separation was carried out by a mobile phase consisting of bidistilled water, tetrahydrofuran and ortho-phosphoric acid (97.7: 1.8: 0.5) (v/v/v). The salicin amount of these samples was analyzed by measuring the peak area at the wavelength, 270 nm. A reversed phase phenyl column (250 x 4.6mm, 5 mu m) was used and flow rate was set to 1 ml/min. in an isocratic elution. The results provided 6 HPLC method was found in agreement with those indicated by European Pharmacopoeia. It was observed that S. babylonica female bark sample possess the highest salicin content (2.675), while S. caprea female bark (0.058) has the lowest salicin content as w/w (%).