Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Subject: search.filters.subject.Caputo DerivativeWoS Q: search.filters.wosQuartile.Q2

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Now showing 1 - 10 of 21
  • Article
    Citation - WoS: 16
    Citation - Scopus: 23
    On Fractional Hamiltonian Systems Possessing First-Class Constraints Within Caputo Derivatives
    (Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Matematik
    The fractional constrained systems possessing only first class constraints are analyzed within Caputo fractional derivatives. It was proved that the fractional Hamilton-Jacobi like equations appear naturally in the process of finding the full canonical transformations. An illustrative example is analyzed.
  • Article
    Citation - Scopus: 61
    Solving Multi-Term Orders Fractional Differential Equations by Operational Matrices of Bps With Convergence Analysis
    (2013) Rostamy, D.; Baleanu, Dumitru; Alipour, M.; Jafari, H.; Baleanu, D.; Matematik
    In this paper, we present a numerical method for solving a class of fractional differential equations (FDEs). Based on Bernstein Polynomials (BPs) basis, new matrices are utilized to reduce the multi-term orders fractional differential equation to a system of algebraic equations. Convergence analysis is shown by several theorems. Illustrative examples are included to demonstrate the validity and applicability of this method.
  • Article
    Citation - WoS: 81
    Citation - Scopus: 94
    The Fractional Dynamics of a Linear Triatomic Molecule
    (Editura Acad Romane, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Defterli, Özlem; Jajarmi, Amin; Defterli, Ozlem; Asad, Jihad H.; Matematik
    In this research, we study the dynamical behaviors of a linear triatomic molecule. First, a classical Lagrangian approach is followed which produces the classical equations of motion. Next, the generalized form of the fractional Hamilton equations (FHEs) is formulated in the Caputo sense. A numerical scheme is introduced based on the Euler convolution quadrature rule in order to solve the derived FHEs accurately. For different fractional orders, the numerical simulations are analyzed and investigated. Simulation results indicate that the new aspects of real-world phenomena are better demonstrated by considering flexible models provided within the use of fractional calculus approaches.
  • Article
    Citation - Scopus: 1
    Analysis of Fractional Fokker-Planck Equation With Caputo and Caputo-Fabrizio Derivatives
    (Univ Craiova, 2021) Cetinkaya, Suleyman; Baleanu, Dumitru; Demir, Ali; Baleanu, Dumitru; Matematik
    This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained. By this method, we constructed the solution of fractional Fokker-Planck equations in Caputo and Caputo-Fabrizio senses. The results show that this method is advantageous and applicable to form the series resolution of the fractional mathematical models.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 31
    A Novel Spectral Approximation for the Two-Dimensional Fractional Sub-Diffusion Problems
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Zaky, M. A.; Baleanu, D.; Abdelkawy, M. A.; Matematik
    This paper reports a new numerical method that enables easy and convenient discretization of a two-dimensional sub-diffusion equation with fractional derivatives of any order. The suggested method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional derivatives, described in the Caputo sense. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. The validity and effectiveness of the method are demonstrated by solving two numerical examples, which are presented in the form of tables and graphs to make more easier comparisons with the exact solutions and the results obtained by other methods.
  • Article
    Citation - WoS: 89
    Citation - Scopus: 124
    New Numerical Approximations for Space-Time Fractional Burgers' Equations Via a Legendre Spectral-Collocation Method
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Zaky, M. A.; Baleanu, D.
    Burgers' equation is a fundamental partial differential equation in fluid mechanics. This paper reports a new space-time spectral algorithm for obtaining an approximate solution for the space-time fractional Burgers' equation (FBE) based on spectral shifted Legendre collocation (SLC) method in combination with the shifted Legendre operational matrix of fractional derivatives. The fractional derivatives are described in the Caputo sense. We propose a spectral shifted Legendre collocation method in both temporal and spatial discretizations for the space-time FBE. The main characteristic behind this approach is that it reduces such problem to that of solving a system of nonlinear algebraic equations that can then be solved using Newton's iterative method. Numerical results with comparisons are given to confirm the reliability of the proposed method for FBE.
  • Article
    Citation - WoS: 25
    Citation - Scopus: 37
    A Solution of the Fractional Differential Equations in the Setting of B-Metric Space
    (Vasyl Stefanyk Precarpathian Natl Univ, 2021) Afshari, H.; Karapinar, E.
    In this paper, we study the existence of solutions for the following differential equations by using a fixed point theorems {D(c)(mu)w(sigma) +/- D(c)(nu)w(sigma) = h(sigma, w(sigma)), sigma is an element of J, 0 < nu < mu < 1, w(0) = w(0), where D-mu, D-nu is the Caputo derivative of order mu, nu, respectively and h: J x R -> R is continuous. The results are well demonstrated with the aid of exciting examples.
  • Article
    Citation - WoS: 31
    Citation - Scopus: 40
    New Solutions of the Fractional Differential Equations With Modified Mittag-Leffler Kernel
    (Asme, 2023) Baleanu, Dumitru; Odibat, Zaid
    This paper is concerned with some features of the modified Caputo-type Mittag-Leffler fractional derivative operator and its associated fractional integral operator. Mainly, new types of solutions for fractional differential equations with Mittag-Leffler kernel are generated based on a numerical algorithm developed in this paper. The suggested algorithm is used to describe the solution behavior of models involving modified Caputo-type Mittag-Leffler fractional derivatives. The results described in this paper are expected to be effectively employed in the area of simulating related fractional models.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 16
    A Robust Scheme for Caputo Variable-Order Time-Fractional Diffusion-Type Equations
    (Springer, 2023) Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Hincal, Evren; Sadri, Khadijeh
    The focus of this work is to construct a pseudo-operational Jacobi collocation scheme for numerically solving the Caputo variable-order time-fractional diffusion-type equations with applications in applied sciences. Modeling scientific phenomena in the context of fluid flow problems, curing reactions of thermosetting systems, solid oxide fuel cells, and solvent diffusion into heavy oils led to the appearance of these equations. For this reason, the numerical solution of these equations has attracted a lot of attention. More precisely, using pseudo-operational matrices and appropriate approximations based on bivariate Jacobi polynomials, the approximate solutions of the variable-order time-fractional diffusion-type equations in the Caputo sense with high accuracy are formally retrieved. Based on orthogonal bivariate Jacobi polynomials and their operational matrices, a sparse algebraic system is generated which makes implementing the proposed approach easy. An error bound is computed for the residual function by proving some theorems. To illustrate the accuracy and efficiency of the scheme, several illustrative examples are considered. The results demonstrate the efficiency of the present method compared to those achieved by the Legendre and Lucas multi-wavelet methods and the Crank-Nicolson compact method.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 17
    A Unifying Computational Framework for Fractional Gross-Pitaevskii Equations
    (Iop Publishing Ltd, 2021) Baleanu, Dumitru; Veeresha, P.
    This paper concerns investigating the complex behaviour of the special case of Schrodinger equation called Gross-Pitaevskii (GP) equations using q-homotopy analysis transform method (q-HATM) with fractional order. Based on denticity function and different initial conditions, we consider three different examples to demonstrate the proficiency of q-HATM. We consider different initial conditions for the hired system and the projected method is elegant unification of q-homotopy analysis algorithm and Laplace transform. Further, the physical natures of the achieved results have been captured for change in space, time, homotopy parameter and fractional order in terms of contour and surface plots, and the accuracy is presented with the numerical study. The obtained results conclude that, the hired technique is highly methodical, easy to implement and accurate to examine the behaviour of the nonlinear equations of both fractional and integer order describing allied areas of science.