Browsing by Author "Prakasha, Doddabhadrappla Gowda"
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Article An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equation(Mdpi, 2019) Veeresha, Pundikala; Baleanu, Dumitru; Prakasha, Doddabhadrappla Gowda; Baleanu, Dumitru; 56389The 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.Article Analysis of Fractional Swift-Hohenberg Equation Using A Novel Computational Technique(Wiley, 2020) Veeresha, Pundikala; Baleanu, Dumitru; Prakasha, Doddabhadrappla Gowda; Baleanu, Dumitru; 56389In 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.