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Browsing by Author "Deniz, Sinan"

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    Article
    Citation Count: Saad, Khaled M.; Deniz, Sinan; Baleanu, Dumitru, "On a new modified fractional analysis of Nagumo equation", International Journal of Biomathematics, Vol. 12, No. 3, (2019).
    On a new modified fractional analysis of Nagumo equation
    (World Scientific Publ CO PTE LTD, 2019) Saad, Khaled M.; Deniz, Sinan; Baleanu, Dumitru; 56389
    In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo-Fabrizio and Atangana-Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called h-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.
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    Article
    Citation Count: Shah, Kamal...et al. (2020). "Qualitative Analysis of a Mathematical Model in the Time of COVID-19", BioMed Research International, Vol. 2020.
    Qualitative Analysis of a Mathematical Model in the Time of COVID-19
    (2020) Shah, Kamal; Abdeljawad, Thabet; Mahariq, Ibrahim; Jarad, Fahd; Deniz, Sinan; 234808
    In this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, its existence must be guaranteed. Therefore, via using the classical fixed point theory, we establish the required results. Also, we present the results of stability of Ulam's type by using the tools of nonlinear analysis. For the semianalytical results, we extend the usual Laplace transform coupled with Adomian decomposition method to obtain the approximate solutions for the corresponding compartments of the considered model. Finally, in order to support our study, graphical interpretations are provided to illustrate the results by using some numerical values for the corresponding parameters of the model.