WoS İndeksli Yayınlar Koleksiyonu

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

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 6
    Citation - Scopus: 7
    A Reliable Mixed Method for Singular Integro-Differential Equations of Non-Integer Order
    (Edp Sciences S A, 2018) Darzi, Rahmat; Agheli, Ahram; Baleanu, Dumitru; Agheli, Bahram
    It is our goal in this article to apply a method which is based on the assumption that combines two methods of conjugating collocation and multiple shooting method. The proposed method can be used to find the numerical solution of singular fractional integro-differential boundary value problems (SFIBVPs) D-upsilon y(t) + eta integral(t)(0) (t - s)(zeta-1) y(s) ds = g(t), 1 < upsilon <= 2, 0 < zeta < 1, eta is an element of R, where D-upsilon denotes the Caputo derivative of order upsilon. Meanwhile, in a separate section the existence and uniqueness of this method is also discussed. Two examples are presented to illustrate the application and further understanding of the methods.
  • Article
    Citation - WoS: 121
    Citation - Scopus: 138
    New Aspects of Fractional Biswas-Milovic Model With Mittag-Leffler Law
    (Edp Sciences S A, 2019) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    This article deals with a fractional extension of Biswas-Milovic (BM) model having Kerr and parabolic law nonlinearities. The BM model plays a key role in describing the long-distance optical communications. The fractional homotopy analysis transform technique (FHATM) is applied to examine the BM equation involving Atangana-Baleanu (AB) derivative of fractional order. The FHATM is constructed by using homotopy analysis technique, Laplace transform algorithm and homotopy polynomials. The numerical simulation work is performed with the aid of maple software package. In order to demonstrate the effects of order of AB operator, variables and parameters on the displacement, the results are shown graphically. The outcomes of the present investigation are very encouraging and show that the AB fractional operator is very useful in mathematical modelling of natural phenomena.
  • Article
    Citation - WoS: 127
    Citation - Scopus: 142
    Modeling the Dynamics of Hepatitis E Via the Caputo-Fabrizio Derivative
    (Edp Sciences S A, 2019) Hammouch, Zakia; Baleanu, Dumitru; Khan, Muhammad Altaf
    A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo-Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams-Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 16
    Bifurcation Analysis of a Modified Tumor-Immune System Interaction Model Involving Time Delay
    (Edp Sciences S A, 2017) Kayan, S.; Merdan, H.; Yafia, R.; Goktepe, S.
    We study stability and Hopf bifurcation analysis of a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a reaction-diffusion system including time delay under the Neumann boundary conditions, and is based on Kuznetsov-Taylor's model. Choosing the delay parameter as a bifurcation parameter, we first show that Hopf bifurcation occurs. Second, we determine two properties of the periodic solution, namely its direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations. Furthermore, we discuss the effects of diffusion on the dynamics by analyzing a model with constant coefficients and perform some numerical simulations to support the analytical results. The results show that diffusion has an important effects on the dynamics of a mathematical model.