Matematik Bölümü Yayın Koleksiyonu
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Article Citation - WoS: 14Citation - Scopus: 17Pulsatile Blood Flow in Constricted Tapered Artery Using a Variable-Order Fractional Oldroyd-B Model(Vinca inst Nuclear Sci, 2017) Azrar, Lahcen; Baleanu, Dumitru; Bakhti, HamzahThe aim of this paper is to deal with the pulsatile flow of blood in stenosed arteries using one of the known constitutive models that describe the viscoelasticity of blood witch is the generalized Oldroyd-B model with a variable-order fractional derivative. Numerical approximation for the axial velocity and wall shear stress were obtained by use of the implicit finite-difference scheme. The velocity profile is analyzed by graphical illustrations. This mathematical model gives more realistic results that will help medical practitioners and it has direct applications in the treatment of cardiovascular diseases.Publication About fractional calculus of singular Lagrangians(IEEE, 2004) Baleanu, DumitruIn this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. Despite of the complexity of solutions in the fractional case the gauge classical symmetry was preserved. Four examples of fractional singular Lagrangians were analyzed in details.Article Citation - WoS: 3Citation - Scopus: 2Fractional Hybrid Initial Value Problem Featuring Q-Derivatives(Comenius Univ, 2019) Baleanu, D.; Baleanu, Dumitru; Darzi, R.; Agheli, B.; MatematikWe have perused about the existence of a solution toward hybrid initial value problem (HIVP) featuring fractional q-derivative {D-q(delta)[v(t)/h(t,v(t) max(0 <=tau <= t)vertical bar v(t)vertical bar] rho(t, v(t)), t is an element of(0,1), 0 < delta <= 1`, in which D-q(delta) denotes the Riemann-Liouville fractional q-derivative in the order of delta. In Banach algebra, by making use of a fi xed point theorem based Dhage along with mixed Lipschitz and Caratheodory condition, a way of solving the above fractional Hybrid initial value problem (FHIVP) featuring q-derivatives veri fi ed, in this study.Article Citation - WoS: 4Citation - Scopus: 4Inverse Problems for the Impulsive Sturm-Liouville Operator With Jump Conditions(Taylor & Francis Ltd, 2019) Kadkhoda, Nematollah; Baleanu, Dumitru; Khalili, YasserThe inverse problem for impulsive Sturm-Liouville operators with discontinuity conditions is considered. We have shown that all parameters used in the boundary conditions as well as can be uniquely established by a set of values of eigenfunctions at the mid-point and one spectrum. Moreover, we discuss Gesztesy-Simon theorem and show that if the potential function is prescribed on the interval for some , then parts of a finite number of spectra suffice to determine on .Article Citation - WoS: 23Citation - Scopus: 22New Analytical Solutions of Heat Transfer Flow of Clay-Water Base Nanoparticles With the Application of Novel Hybrid Fractional Derivative(Vinca inst Nuclear Sci, 2020) Ikram, Muhammad Danish; Ali, Rizwan; Baleanu, Dumitru; Alshomrani, Ali S.; Asjad, Muhammad ImranClay nanoparticles are hanging in three different based fluids (water, kerosene, and engine oil). The exact terminologies of Maxwell-Garnett and Brinkman for the current thermophysical properties of clay nanofluids are used, while the flow occurrence is directed by a set linear PDE with physical initial and boundary conditions. The classical governing equations are extended to non-integer order hybrid fractional derivative which is introduced in [33]. Analytical solutions for temperature and velocity fields are attained via Laplace transform technique. Some limiting solutions are also obtained from the existing literature and compared for different values of fractional parameter. To vision the impact of several flow parameters on the temperature and velocity some graphs are drawn using Mathcad software and designed in different figures. As a result, we found that hybrid fractional model is better in describing the decay behavior of temperature and velocity in comparison of classical derivatives. In comparison of nanofluid with different base fluids, it is concluded that water-based nanofluid has higher velocity than others.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: 1Citation - Scopus: 1Fractional Heat Equation Optimized by a Chaotic Function(Vinca inst Nuclear Sci, 2021) Wazi, Mayada T.; Baleanu, Dumitru; Al-Saidi, Nadia; Ibrahim, Rabha W.In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function.Article Citation - WoS: 10Citation - Scopus: 9Bright, Dark, and Singular Optical Soliton Solutions for Perturbed Gerdjikov-Ivanov Equation(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Kumar, Sunil; Ulutas, EsmaThis study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this equation that models pulse dynamics in optical fibers. It is retrieved some bright, dark optical and singular solitons profile in the limiting cases of the Jacobi elliptic functions. The constraint conditions depending on the parameters for the existence of solitons are also presented.Article Citation - WoS: 1Citation - Scopus: 1Solving Existence Problems Via F-Contraction in Modified B-Metric Spaces(Turkic World Mathematical Soc, 2022) Karapinar, E.; Karapınar, Erdal; Sedghi, S.; Shobe, N.; MatematikIn this paper, we introduce a new abstract structure, expanded b-metric, as an natural extension of b-metric. We also define basic topological notions in expanded b -metric to able to investigate the existence of fixed point for such mappings under various F-contractive conditions. We provide example to illustrate the results presented herein.Article Citation - WoS: 1Citation - Scopus: 2Exploration of Casson Fluid-Flow Along Exponential Heat Source in a Thermally Stratified Porous Media(Vinca inst Nuclear Sci, 2023) Dadheech, Praveen Kumar; Jat, Ram Niwas; Baleanu, Dumitru; Purohit, Sunil Dutt; Agrawal, PriyankaObjective of the present investigation is intended to study the MHD Casson fluids flow through an exponentially stretching surface. This free convective flow is in-vestigated in thermally stratified porous medium. Also viscosity along with thermal conductivity is varying with temperature. With the exponential decay for the inter-nal heat generation in the region and buoyancy force, the natural-convection is induced. Then the transformed set of equations of the flow after applying suitable similarity solutions were encountered by Shooting Technique in conjunction with the fourth ordered Runge-Kutta method. Outputs illustrates that with increased viscosity parameter an increasing velocity profile is noticed but a decrement is observed for temperature field in entire domain and near the wall for temperature gradient profile. Also with increased Casson fluids parameter decreasing velocity profile is noticed but an increment is observed for temperature field in entire do-main and for temperature gradient profile near the wall.Article Citation - WoS: 38Citation - Scopus: 30Prabhakar Fractional Derivative and Its Applications in the Transport Phenomena Containing Nanoparticles(Vinca inst Nuclear Sci, 2021) Zahid, Muhammad; Chu, Yu-Ming; Baleanu, Dumitru; Asjad, Muhammad ImranIn this paper, a new approach of analytical solutions is carried out on the thermal transport phenomena of Brinkman fluid based on Prabhakar's fractional derivative with generalized Fourier's law. The governing equations are obtained through constitutive relations and analytical solutions obtained via Laplace transform technique. Solutions for temperature and velocity field were analyzed through graphical description by MathCad software. The fluid properties revealed various aspects for different flow parameters as well as fractional parameter values and found important results. As a result, it is found that fluid properties can be enhanced by increasing the values of fractional parameters and can be useful in some experimental data where suitable.Article Citation - WoS: 3161Citation - Scopus: 3292New Fractional Derivatives With Non-Local and Non-Singular Kernel Theory and Application To Heat Transfer Model(Vinca inst Nuclear Sci, 2016) Baleanu, Dumitru; Atangana, AbdonIn this paper a new fractional derivative with non-local and no-singular kernel is proposed. Some useful properties of the new derivative are presented and applied to solve the fractional heat transfer model.Article Citation - Scopus: 1Global Stability, Periodicity, and Bifurcation Analysis of a Difference Equation(Aip Publishing, 2023) Manuel, M. Maria Susai; Baleanu, Dumitru; Dilip, D. S.; Amalraj, J. LeoThis research aims to discuss the existence, global stability, periodicity, and bifurcation analysis of a modified version of the ecological model proposed by Tilman and Wedlin [Nature 353, 653-655 (1991)].Article Chemometric Calibration Based on the Wavelet Transform for the Quantitative Resolution of Two-Colorant Mixtures(Editura Acad Romane, 2005) Baleanu, Dumitru; Dinç, E; Baleanu, D; Taş, Kenan; Üstundag, O; Tas, K; MatematikIn this study we proposed a wavelet transform (WT) followed by two chemometric techniques for the quantitative determination of sunset yellow (SUN) and tartrazine (TAR) in their market samples. Absorbances of the concentration set formed by TAR and SUN mixtures were measured between 335-575 nm at 480 points with 0.5 nm intervals and their absorbance values as absorbance data vectors were transferred into the wavelets domain. A continuous wavelet transform (CWT) was applied, to the absorbance data. The obtained CWT-coefficients (x-block) and concentration set (y-block) were used for the construction of the principal component regression (VCR) and partial least squares (PLS) calibrations. Good results were reported for the application of the combining wavelets and chemometric tools in the determination of colorants in samples.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.Editorial Advanced Modelling of Transport Problems in Heat-Mass and Related Fluid Mechanics(Vinca inst Nuclear Sci, 2021) Hristov, Jordan; Baleanu, Dumitru; Kumar, Devendra; Baleanu, Dumitru; MatematikEditorial Contemporary Modelling Methods in Heat, Mass, and Fluid Flow - Second Part(Vinca inst Nuclear Sci, 2017) Hristov, Jordan; Baleanu, Dumitru; Baleanu, Dumitru; Atangana, Abdon; MatematikArticle Citation - WoS: 1Citation - Scopus: 2Motion of a Spherical Particle in a Rotating Parabola Using Fractional Lagrangian(Univ Politehnica Bucharest, Sci Bull, 2017) Baleanu, D.; Baleanu, Dumitru; Asad, J. H.; Alipour, M.; Blaszczyk, T.; MatematikIn this work, the fractional Lagrangian of a particle moving in a rotating parabola is used to obtain the fractional Euler- Lagrange equations of motion where derivatives within it are given in Caputo fractional derivative. The obtained fractional Euler- Lagrange equations are solved numerically by applying the Bernstein operational matrices with Tau method. The results obtained are very good and when the order of derivative closes to 1, they are in good agreement with those obtained in Ref. [10] using Multi step- Differential Transformation Method (Ms-DTM).Article On Singular Fifth-Order Boundary Value Problems With Deficiency Indices (5, 5)(Math Soc Serbia-drustvo Matematicara Srbije, 2022) Uğurlu, Ekin; Ugurlu, Ekin; Tas, Kenan; Taş, Kenan; MatematikThis paper is devoted to introduce a way of construction of the well-defined boundary conditions for the solutions of a singular fifth-order equation with deficiency indices (5, 5). Imposing suitable separated and coupled boundary conditions some properties of the eigenvalues of the problems have been investigated.Article Citation - WoS: 5Citation - Scopus: 6Spectrophotometric Simultaneous Analysis of Two-Component Mixture by Bivariate and Multivariate Calibrations Using the Linear Regression Functions(Editura Acad Romane, 2008) Dinc, Erdal; Baleanu, Dumitru; Arslan, Fahrettin; Baleanu, Dumitru; MatematikSpectral bivariate calibration (SBC) and spectral multivariate calibration (SMC) approaches based on the linear regression models were applied to the simultaneous determination of chlorzoxazone (CHL) and paracetamol (PAR) in tablets. SBC model was constructed by using four linear regression functions at two-wavelength set (220 and 244 nm) selecting two optimal wavelengths among 25 wavelength points. SMC model for cacti compound was obtained by using of 50 linear regression functions at 25 wavelength points in the spectral range 220-293 nm without selecting any optimal wavelength points. SBC and SMC was validated by using an independent validation set containing CHL-PAR combinations in the linear concentration range. The recovery results were found between 100.6% and 102.6% for both proposed appropaches, therefore we Conclude that a successuful method application was reported. The results obtained in this study clearly indicate that the proposed SBC and SMC approaches are suitable to be used for the quality control and routine analysis of the commercial tablets containing CHL and PAR compounds.
