Scopus İndeksli Yayınlar Koleksiyonu

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

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Now showing 1 - 6 of 6
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Computational Investigation of Hand Foot Mouth Disease Dynamics With Fuzziness
    (Tech Science Press, 2023) Dayan, Fazal; Ahmed, Nauman; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; Baleanu, Dumitru
    The first major outbreak of the severely complicated hand, foot and mouth disease (HFMD), primarily caused by enterovirus 71, was reported in Taiwan in 1998. HFMD surveillance is needed to assess the spread of HFMD. The parameters we use in mathematical models are usually classical mathematical parameters, called crisp parameters, which are taken for granted. But any biological or physical phenomenon is best explained by uncertainty. To represent a realistic situation in any mathematical model, fuzzy parameters can be very useful. Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling. However, few works use fuzzy theory in building models to simulate HFMD dynamics. In this context, we examined an HFMD model with fuzzy parameters. A Non Standard Finite Difference (NSFD) scheme is developed to solve the model. The developed technique retains essential properties such as positivity and dynamic consistency. Numerical simulations are presented to support the analytical results. The convergence and consistency of the proposed method are also discussed. The proposed method converges unconditionally while the many classical methods in the literature do not possess this property. In this regard, our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 23
    Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation
    (Tech Science Press, 2021) Abbas, Muhammad; Baleanu, Dumitru; Iqbal, Muhammad Kashif; Riaz, Muhammad Bilal; Amin, Muhammad
    This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 15
    Numerical Investigation of Space Fractional Order Diffusion Equation by the Chebyshev Collocation Method of the Fourth Kind and Compact Finite Difference Scheme
    (Amer inst Mathematical Sciences-aims, 2021) Safdari, Hamid; Azari, Yaqub; Jafari, Hossein; Baleanu, Dumitru; Aghdam, Yones Esmaeelzade
    This paper develops a numerical scheme for finding the approximate solution of space fractional order of the diffusion equation (SFODE). Firstly, the compact finite difference (CFD) with convergence order O(delta tau 2) is used for discretizing time derivative. Afterwards, the spatial fractional derivative is approximated by the Chebyshev collocation method of the fourth kind. Furthermore, time-discrete stability and convergence analysis are presented. Finally, two examples are numerically investigated by the proposed method. The examples illustrate the performance and accuracy of our method compared to existing methods presented in the literature. 1. Introduction. One of the issues which have garnered researchers' attention these days is the fractional differential equations (FDEs) and have been numerically investigated by a huge number of authors [2, 3, 8, 9, 16, 21, 23, 25, 28, 29]. Fractional calculus is involved in many applications of science and engineering such as economics, physics, optimal control, and other applications, see [10, 11, 13, 19, 22, 26, 33, 34, 35]. A case in point is the diffusion and reaction-diffusion models in
  • Article
    Citation - WoS: 19
    Citation - Scopus: 20
    Numerical Control Measures of Stochastic Malaria Epidemic Model
    (Tech Science Press, 2020) Ahmadian, Ali; Raza, Ali; Baleanu, Dumitru; Ahsan, Muhammad Sarwar; Sathar, Mohammad Hasan Abdul; Rafiq, Muhammad
    Nonlinear stochastic modeling has significant role in the all discipline of sciences. The essential control measuring features of modeling are positivity, boundedness and dynamical consistency. Unfortunately, the existing stochastic methods in literature do not restore aforesaid control measuring features, particularly for the stochastic models. Therefore, these gaps should be occupied up in literature, by constructing the control measuring features numerical method. We shall present a numerical control measures for stochastic malaria model in this manuscript. The results of the stochastic model are discussed in contrast of its equivalent deterministic model. If the basic reproduction number is less than one, then the disease will be in control while its value greater than one shows the perseverance of disease in the population. The standard numerical procedures are conditionally convergent. The propose method is competitive and preserve all the control measuring features unconditionally. It has also been concluded that the prevalence of malaria in the human population may be controlled by reducing the contact rate between mosquitoes and humans. The awareness programs run by world health organization in developing countries may overcome the spread of malaria disease.
  • 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: 11
    Citation - Scopus: 13
    On Solving Fractional Mobile/Immobile Equation
    (Sage Publications Ltd, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Pourbashash, Hossein
    In this article, a numerical efficient method for fractional mobile/immobile equation is developed. The presented numerical technique is based on the compact finite difference method. The spatial and temporal derivatives are approximated based on two difference schemes of orders O(T2-alpha) and O(h(4)), respectively. The proposed method is unconditionally stable and the convergence is analyzed within Fourier analysis. Furthermore, the solvability of the compact finite difference approach is proved. The obtained results show the ability of the compact finite difference.