Matematik Bölümü Yayın Koleksiyonu

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

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Author: search.filters.author.Al Qurashi, Maysaa MohamedPublisher: search.filters.publisher.Mdpi

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations
    (Mdpi, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas; Acan, Omer
    In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 32
    Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations With Riesz Derivative
    (Mdpi, 2018) Baleanu, Dumitru; Huang, Jianfei; Al Qurashi, Maysaa Mohamed; Tang, Yifa; Zhao, Yue; Arshad, Sadia
    In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grunwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation. Then, the integral is approximated by the trapezoidal formula. Further, the stability and convergence analysis are discussed rigorously. The resulting scheme is formally proved with the second order accuracy both in space and time. Numerical experiments are also presented to verify the theoretical analysis.
  • Article
    Citation - WoS: 45
    Citation - Scopus: 60
    Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators With New Fractional Differentiation
    (Mdpi, 2017) Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Cordova-Fraga, Teodoro; Fabricio Escobar-Jimenez, Ricardo; Olivares-Peregrino, Victor H.; Al Qurashi, Maysaa Mohamed; Coronel-Escamilla, Antonio; Gómez-Aguilar, José Francisco; Escobar-Jiménez, Ricardo Fabricio
    In this work, the study of the fractional behavior of the Bateman-Feshbach-Tikochinsky and Caldirola-Kanai oscillators by using different fractional derivatives is presented. We obtained the Euler-Lagrange and the Hamiltonian formalisms in order to represent the dynamic models based on the Liouville-Caputo, Caputo-Fabrizio-Caputo and the new fractional derivative based on the Mittag-Leffler kernel with arbitrary order . Simulation results are presented in order to show the fractional behavior of the oscillators, and the classical behavior is recovered when is equal to 1.
  • Article
    Citation - WoS: 75
    Citation - Scopus: 110
    Analytical Solutions of the Electrical Rlc Circuit Via Liouville-Caputo Operators With Local and Non-Local Kernels
    (Mdpi, 2016) Fabian Morales-Delgado, Victor; Antonio Taneco-Hernandez, Marco; Baleanu, Dumitru; Fabricio Escobar-Jimenez, Ricardo; Mohamed Al Qurashi, Maysaa; Francisco Gomez-Aguilar, Jose; Taneco-Hernández, Marco Antonio; Al Qurashi, Maysaa Mohamed; Morales-Delgado, Victor Fabian; Gómez-Aguilar, José Francisco; Escobar-Jiménez, Ricardo Fabricio
    In this work we obtain analytical solutions for the electrical RLC circuit model defined with Liouville-Caputo, Caputo-Fabrizio and the new fractional derivative based in the Mittag-Leffler function. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source terms are considered in the fractional differential equations. The classical behaviors are recovered when the fractional order a is equal to 1.