Browsing by Author "Veeresha, Pundikala"

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An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equation
(Mdpi, 2019) Veeresha, Pundikala; Baleanu, Dumitru; Prakasha, Doddabhadrappla Gowda; Baleanu, Dumitru; 56389
The q-homotopy analysis transform method (q-HATM) is employed to find the solution for the fractional Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with two of them having Jacobi elliptic functions. The numerical simulations have been conducted to verify that the proposed scheme is reliable and accurate. Moreover, the uniqueness and convergence analysis for the projected problem is also presented. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyze the complex problems arising in science and technology.
Analysis of Fractional Swift-Hohenberg Equation Using A Novel Computational Technique
(Wiley, 2020) Veeresha, Pundikala; Baleanu, Dumitru; Prakasha, Doddabhadrappla Gowda; Baleanu, Dumitru; 56389
In this paper, the approximated analytical solution for fractional Swift-Hohenberg (S-H) equation is found with the aid of novel technique called q-homotopy analysis transform method (q-HATM). To ensure the applicability and efficiency of the proposed algorithm, we consider non-linear arbitrary-order S-H equation in presence and absence of dispersive term. The convergence analysis for the projected problem is presented, and the numerical simulations have been conducted to verify the future scheme is reliable and accurate. Further, the effect of bifurcation and dispersive parameters with physical importance on the probability density function for distinct fractional Brownian and standard motions are presented through plots. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyse the complex problems that arose in science and technology.
Design of a fractional-order atmospheric model via a class of ACT-like chaotic system and its sliding mode chaos control
(2023) Baleanu, Dumitru; Baishya, Chandrali; Veeresha, Pundikala; Baleanu, Dumitru; 56389
Investigation of the dynamical behavior related to environmental phenomena has received much attention across a variety of scientific domains. One such phenomenon is global warming. The main causes of global warming, which has detrimental effects on our ecosystem, are mainly excess greenhouse gases and temperature. Looking at the significance of this climatic event, in this study, we have connected the ACT-like model to three climatic components, namely, permafrost thaw, temperature, and greenhouse gases in the form of a Caputo fractional differential equation, and analyzed their dynamics. The theoretical aspects, such as the existence and uniqueness of the obtained solution, are examined. We have derived two different sliding mode controllers to control chaos in this fractional-order system. The influences of these controllers are analyzed in the presence of uncertainties and external disturbances. In this process, we have obtained a new controlled system of equations without and with uncertainties and external disturbances. Global stability of these new systems is also established. All the aspects are examined for commensurate and non-commensurate fractional-order derivatives. To establish that the system is chaotic, we have taken the assistance of the Lyapunov exponent and the bifurcation diagram with respect to the fractional derivative. To perform numerical simulation, we have identified certain values of the parameters where the system exhibits chaotic behavior. Then, the theoretical claims about the influence of the controller on the system are established with the help of numerical simulations.