Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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

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Now showing 1 - 9 of 9
  • Article
    Citation - WoS: 46
    Citation - Scopus: 48
    Solutions of the Fractional Davey-Stewartson Equations With Variational Iteration Method
    (Editura Acad Romane, 2012) Baleanu, Dumitru; Jafari, Hossain; Kadem, Abdelouahab; Yılmaz, Tuğba; Baleanu, Dumitru; Yilmaz, Tugba; Matematik; Psikoloji
    This paper presents approximate analytical solutions for the fractional Davey-Stewartson equations using the Variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. The results obtained by this method have been compared with the exact solutions and show that the introduced approach is a promising tool for solving many linear and nonlinear fractional differential equations.
  • Article
    Citation - WoS: 52
    Citation - Scopus: 54
    Fractional Caputo Heat Equation Within the Double Laplace Transform
    (Editura Acad Romane, 2013) Jarad, Fahd; Anwar, A. M. O.; Jarad, Fahd; Baleanu, Dumitru; Baleanu, D.; Ayaz, F.; Matematik
    The heat equation and its fractional generalization are used in various applications in science and engineering. In this paper firstly we introduce the double Laplace transform of the partial fractional integrals and derivatives which can be used to solve partial differential equations with Caputo fractional derivatives. Secondly, the fractional heat equation was investigated in details with the help of this new generalized transform
  • Article
    Citation - WoS: 40
    Citation - Scopus: 41
    Numerical Treatment of Time-Fractional Klein-Gordon Equation Using Redefined Extended Cubic B-Spline Functions
    (Frontiers Media Sa, 2020) Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Amin, Muhammad
    In this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein-Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order alpha is an element of (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme isO(h(2)+ Delta t(2-alpha)) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.
  • Article
    Citation - WoS: 53
    Citation - Scopus: 58
    An Efficient Computational Technique for Fractional Model of Generalized Hirota-Satsuma Korteweg-De Vries and Coupled Modified Korteweg-De Vries Equations
    (Asme, 2020) Prakasha, D. G.; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Veeresha, P.
    The aim of the present investigation to find the solution for fractional generalized Hirota-Satsuma coupled Korteweg-de-Vries (KdV) and coupled modified KdV (mKdV) equations with the aid of an efficient computational scheme, namely, fractional natural decomposition method (FNDM). The considered fractional models play an important role in studying the propagation of shallow-water waves. Two distinct initial conditions are choosing for each equation to validate and demonstrate the effectiveness of the suggested technique. The simulation in terms of numeric has been demonstrated to assure the proficiency and reliability of the future method. Further, the nature of the solution is captured for different value of the fractional order. The comparison study has been performed to verify the accuracy of the future algorithm. The achieved results illuminate that, the suggested computational method is very effective to investigate the considered fractional-order model.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 16
    An Avant-Garde Handling of Temporal-Spatial Fractional Physical Models
    (Walter de Gruyter Gmbh, 2020) Alquran, Marwan; Katatbeh, Qutaibeh; Yousef, Feras; Momani, Shaher; Baleanu, Dumitru; Jaradat, Imad
    In the present study, we dilate the differential transform scheme to develop a reliable scheme for studying analytically the mutual impact of temporal and spatial fractional derivatives in Caputo's sense. We also provide a mathematical framework for the transformed equations of some fundamental functional forms in fractal 2-dimensional space. To demonstrate the effectiveness of our proposed scheme, we first provide an elegant scheme to estimate the (mixed-higher) Caputo-fractional derivatives, and then we give an analytical treatment for several (non)linear physical case studies in fractal 2-dimensional space. The study concluded that the proposed scheme is very efficacious and convenient in extracting solutions for wide physical applications endowed with two different memory parameters as well as in approximating fractional derivatives.
  • Article
    Citation - WoS: 44
    Citation - Scopus: 49
    A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships
    (Mdpi, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, Jagdev
    In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian's decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter h and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    On the Kolmogorov Forward Equations Within Caputo and Riemann-Liouville Fractions Derivatives
    (Ovidius Univ Press, 2016) Baleanu, Dumitru; Alipour, Mohsen
    In this work, we focus on the fractional versions of the well-known Kolmogorov forward equations. We consider the problem in two cases. In case 1, we apply the left Caputo fractional derivatives for alpha is an element of (0, 1] and in case 2, we use the right Riemann-Liouville fractional derivatives on R+, for alpha is an element of (1, + infinity). The exact solutions are obtained for the both cases by Laplace transforms and stable subordinators.
  • Article
    Citation - WoS: 125
    Citation - Scopus: 136
    On Nonlinear Fractional Klein-Gordon Equation
    (Elsevier, 2011) Golmankhaneh, Ali K.; Baleanu, Dumitru; Golmankhaneh, Alireza K.
    Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Cordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order a are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.
  • Article
    On nonlinear fractional Klein-Gordon equation
    (Elsevier Science Bv, 2011) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
    Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Cordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order a are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation