Scopus İndeksli Yayınlar Koleksiyonu

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

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COAR Access Rights: search.filters.coarAccessRights.metadata only accessSubject: search.filters.subject.Adomian Decomposition Method

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  • Article
    Citation - WoS: 105
    Citation - Scopus: 111
    Approximate Solutions for Diffusion Equations on Cantor Space-Time
    (Editura Acad Romane, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Zhong, Wei-Ping; Matematik
    In this paper we investigate diffusion equations on Cantor space-time and we obtain approximate solutions by using the local fractional Adomian decomposition method derived from the local fractional operators. Analytical solutions are given in terms of the Mittag-Leffler functions defined on Cantor sets.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 11
    Exact Solution for Nonlinear Local Fractional Partial Differential Equations
    (Shahid Chamran Univ Ahvaz, Iran, 2020) Cherif, Mountassir Hamdi; Baleanu, Dumitru; Belghaba, Kacem; Ziane, Djelloul
    In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples and the results obtained, showed the flexibility of applying this algorithm, and therefore, it can be applied to similar examples.
  • Article
    Citation - WoS: 211
    Citation - Scopus: 242
    Chaos Analysis and Asymptotic Stability of Generalized Caputo Fractional Differential Equations
    (Pergamon-elsevier Science Ltd, 2017) Wu, Guo-Cheng; Zeng, Sheng-Da; Baleanu, Dumitru
    This paper investigates chaotic behavior and stability of fractional differential equations within a new generalized Caputo derivative. A semi-analytical method is proposed based on Adomian polynomials and a fractional Taylor series. Furthermore, chaotic behavior of a fractional Lorenz equation are numerically discussed. Since the fractional derivative includes two fractional parameters, chaos becomes more complicated than the one in Caputo fractional differential equations. Finally, Lyapunov stability is defined for the generalized fractional system. A sufficient condition of asymptotic stability is given and numerical results support the theoretical analysis. (C) Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 16
    Approximate Solutions To the Conformable Rosenau-Hyman Equation Using the Two-Step Adomian Decomposition Method With Pade Approximation
    (Wiley, 2020) Aliyu, Aliyu Isa; Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Akgul, Ali
    This paper adopts the Adomian decomposition method and the Pade approximation techniques to derive the approximate solutions of a conformable Rosenau-Hyman equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing both the analytic and approximate solutions.