WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Publisher: search.filters.publisher.MdpiSubject: search.filters.subject.Caputo Fractional Derivative

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  • Article
    Citation - WoS: 27
    Citation - Scopus: 56
    Exact Solution of Two-Dimensional Fractional Partial Differential Equations
    (Mdpi, 2020) Jassim, Hassan Kamil; Baleanu, Dumitru
    In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations.
  • 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.