Matematik Bölümü Yayın Koleksiyonu

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

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Subject: search.filters.subject.ConvergenceWoS Q: search.filters.wosQuartile.Q2

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  • Article
    Citation - WoS: 15
    Design and Numerical Analysis of Fuzzy Nonstandard Computational Methods for the Solution of Rumor Based Fuzzy Epidemic Model
    (Elsevier, 2022) Rafiq, Muhammad; Ahmed, Nauman; Baleanu, Dumitru; Raza, Ali; Ahmad, Muhammad Ozair; Iqbal, Muhammad; Dayan, Fazal
    This model extends the classical epidemic model for cyber consumerism by introducing fuzziness to the model. Fuzziness arises due to insufficient knowledge, experimental errors, operating conditions and parameters that provide inaccurate information. The concepts of confused, escapers and recovered consumers are uncertain due to the different degrees of confusion, escaping and recovery among the individuals of the cyber consumers. The differences can arise, when the cyber consumers under the consideration having distinct habits, customs and different age groups have different degrees of resistance, etc. The chance of transmission of rumors and recovery rates are considered as fuzzy numbers. A rumor-free and two rumor existing-endemic equilibrium points have been derived for the studied model. The model is then solved numerically with fuzzy forward Euler and fuzzy nonstandard finite difference (FNSFD) methods respectively. The numerical and simulation results show that the proposed FNSFD technique is an efficient and reliable tool to deal with such type of dynamical system. (c) 2022 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Travelling Wave Solutions: a New Approach To the Analysis of Nonlinear Physical Phenomena
    (de Gruyter Poland Sp Z O O, 2014) Baleanu, Dumitru; Fardi, Mojtaba; Sayevand, Khosro
    In this manuscript, a reliable scheme based on a general functional transformation is applied to construct the exact travelling wave solution for nonlinear differential equations. Our methodology is investigated by means of the modified homotopy analysis method which contains two convergence-control parameters. The obtained results reveal that the proposed approach is a very effective. Several illustrative examples are investigated in detail.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations
    (Global Science Press, 2018) Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Zhao, Yue; Arshad, Sadia
    A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the L-2 -norm are shown to be O(tau(2) + h(4)), where tau and h are time and space mesh sizes. Numerical examples confirm theoretical results.