Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
10 results
Search Results
Article 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 Citation - WoS: 32Citation - Scopus: 33Lie Symmetry Analysis and Exact Solutions of the Time Fractional Gas Dynamics Equation(Natl inst Optoelectronics, 2016) Hashemi, M. S.; Baleanu, Dumitru; Baleanu, D.; MatematikFinding the symmetries of a given fractional differential equation is a hot topic in the field of fractional differentiation and its applications. In this manuscript, the Lie symmetries of the time fractional gas dynamics (TFGD) equation are analyzed and new exact solutions are obtained.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 - Scopus: 8Mhd Flow and Heat and Mass Transport Investigation Over a Decelerating Disk With Ohmic Heating and Diffusive Effect(Serbian Society of Heat Transfer Engineers, 2023) Mehta, R.; Mehta, T.; Singh, J.; Baleanu, D.; Jain, R.The motive of this study is to investigate the spinning fluid-flow due to revolving disk for the magnetic unsteady Brownian motion of viscous nanofluid. Here the disk is assumed to have an inverse linear angular velocity. In this paper mass transfer is incorporated in the analysis with the existing problem. The array of equation for the unsteady flow firstly converted into dimensionless non-linear equation using appropriate transformation and then the dimensionless system of equation is further solved numerically utilizing MAPLE software. The different emerging parameters mainly magnetic parameter, variable viscosity, Prandtl number, Eckert number, thermophoresis, and Brownian motion parameter has been investigated through graphs and shown in tabular form also. © 2023 Society of Thermal Engineers of Serbia Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditionsArticle Citation - WoS: 118Citation - Scopus: 132Novel Fractional-Order Lagrangian To Describe Motion of Beam on Nanowire(Polish Acad Sciences inst Physics, 2021) Godwe, E.; Erturk, V. S.; Baleanu, D.; Kumar, P.; Asad, J.; Jajarmi, A.Our aim in this research is to investigate the motion of a beam on an internally bent nanowire by using the fractional calculus theory. To this end, we first formulate the classical Lagrangian which is followed by the classical Euler-Lagrange equation. Then, after introducing the generalized fractional Lagrangian, the fractional Euler-Lagrange equation is provided for the motion of the considered beam on the nanowire. An efficient numerical scheme is introduced for implementation and the simulation results are reported for different fractional-order values and various initial settings. These results indicate that the fractional responses approach the classical ones as the fractional order goes to unity. In addition, the fractional Euler-Lagrange equation provides a flexible model possessing more information than the classical description the fact that leads to a considerably better evaluation of the hidden features of the real system under investigation.Article Citation - Scopus: 20New Optical Soliton Solutions of Space-Time Fractional Nonlinear Dynamics of Microtubules Via Three Integration Schemes(IOS Press, 2020) Abdou, M.A.; Abdel-Aty, A.-H.; Ibraheem, A.A.; Nekhili, R.; Baleanu, D.; Owyed, S.In this study, we implement three efficient integration algorithms to retrieve the solutions of optical soliton space-time fractional nonlinear equation for the dynamics of microtubules MTs, which considered as one of the most important part in cellular processes biology. In this work we used three integration methods, firstly, the method of exp(-O)-expansion equation function, secondly the Kudryashov equation method in the general case and the method of extended Bernoulli sub-equation function, with the help of the fractional complex transformation and conformable derivatives which including the solution of complex function, rational function, hyperbolic function and exponential function. Finally, our results give good solution and understanding of the properties of the non-linear waves in fractional medium. © 2020-IOS Press and the authors. All rights reserved.Article Citation - WoS: 23Citation - Scopus: 29Diffraction From Fractal Grating Cantor Sets(Taylor & Francis Ltd, 2016) Baleanu, D.; Golmankhaneh, Alireza K.In this paper, we have generalized the Fa-calculus by suggesting Fourier and Laplace transformations of the function with support of the fractals set which are the subset of the real line. Using this generalization, we have found the diffraction fringes from the fractal grating Cantor sets.Article Citation - WoS: 3Citation - Scopus: 4Existence Results for Fractional Evolution Systems With Riemann-Liouville Fractional Derivatives and Nonlocal Conditions(Ios Press, 2017) Arjunan, M. Mallika; Mallika, D.; Baleanu, D.; Kalamani, P.; Baleanuy, D.; Mallika Arjunan, M.Based on concepts for semigroup theory, fractional calculus, Banach contraction principle and Krasnoselskii fixed point theorem (FPT), this manuscript is principally involved with existence results of Riemann-Liouville (RL) fractional neutral integro-differential systems (FNIDS) with nonlocal conditions (NLCs) in Banach spaces. An example is offered to demonstrate the theoretical concepts.Article Citation - WoS: 82Citation - Scopus: 86The Motion of a Bead Sliding on a Wire in Fractional Sense(Polish Acad Sciences inst Physics, 2017) Jajarmi, A.; Asad, J. H.; Blaszczyk, T.; Baleanu, D.In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical Euler-Lagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grunwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement.Article Citation - WoS: 9Citation - Scopus: 10Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform(Polish Acad Sciences inst Physics, 2016) Blaszczyk, T.; Asad, J. H.; Alipour, M.; Baleanu, D.; Alipoure, M.We investigate the fractional harmonic oscillator on a moving platform. We obtained the fractional Euler-Lagrange equation from the derived fractional Lagrangian of the system which contains left Caputo fractional derivative. We transform the obtained differential equation of motion into a corresponding integral one and then we solve it numerically. Finally, we present many numerical simulations.