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Browsing by Author "Ramachandran, Raja"

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    Citation Count: Anbalagan, Pratap...et al. (2021). "A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks", AIMS Mathematics, Vol. 6, No. 5, pp. 4526-4555.
    A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks
    (2021) Anbalagan, Pratap; Hincal, Evren; Ramachandran, Raja; Baleanu, Dumitru; Cao, Jinde; Niezabitowski, Michal; 56389
    This manuscript is concerned with the stability and synchronization for fractional-order delayed gene regulatory networks (FODGRNs) via Razumikhin approach. First of all, the existence of FODGRNs are established by using homeomorphism theory, 2-norm based on the algebraic method and Cauchy Schwartz inequality. The uniqueness of this work among the existing stability results are, the global Mittag-Letter stability of FODGRNs is explored based on the fractional-order Lyapunov Razumikhin approach. In the meanwhile, two different controllers such as linear feedback and adaptive feedback control, are designed respectively. With the assistance of fractional Razumikhin theorem and our designed controllers, we have established the global Mittag-Letter synchronization and adaptive synchronization for addressing master-slave systems. Finally, three numerical cases are given to justify the applicability of our stability and synchronization results.
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    Article
    Citation Count: Jose, Sayooj Aby...et.al. (2023). "Computational dynamics of a fractional order substance addictions transfer model with Atangana-Baleanu-Caputo derivative", Mathematical Methods in the Applied Sciences, Vol.46, No.5, pp.5060-5085.
    Computational dynamics of a fractional order substance addictions transfer model with Atangana-Baleanu-Caputo derivative
    (2023) Jose, Sayooj Aby; Ramachandran, Raja; Baleanu, Dumitru; Panigoro, Hasan S.; Alzabut, Jehad; Balas, Valentina E.; 56389
    In this paper, the ABC fractional derivative is used to provide a mathematical model for the dynamic systems of substance addiction. The basic reproduction number is investigated, as well as the equilibrium points' stability. Using fixed point theory and nonlinear analytic techniques, we verify the theoretical results of solution existence and uniqueness for the proposed model. A numerical technique for getting the approximate solution of the suggested model is established by using the Adams type predictor-corrector rule for the ABC-fractional integral operator. There are several numerical graphs that correspond to different fractional orders. Furthermore, we present a numerical simulation for the transmission of substance addiction in two scenarios with fundamental reproduction numbers greater than and fewer than one.