Faculty of Natural Sciences and Mathematics
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Item type:Publication, Comparison of two numerical methods for fractional-order Rӧssler system(2020); ; In this paper, we numerically study the chaotic behavior of the fractional-order Rossler system comparing the numerical solutions of the system with Adams-Bashforth-Moulton method (FABM) and Fractional Multistep Differential Transformation method (FMDTM). The fractional derivatives are described in the Caputo sense. FABM method acts like a predictor-corrector pair compared with FMDTM, which is a semi-numerical method that exploits the power-series representation of the solution. Numerically obtained results are analyzed to compare the different integration algorithms. We quantify the distinction between the methods for arbitrary chosen system parameters in the chaotic regime. We have shown numerically that the difference between the results is less pronounced as the value of the fractional-order becomes closer to one. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Numerical solution and chaotic dynamics of fractional order Lorentz and Chen systems(2019); - Some of the metrics are blocked by yourconsent settings
Item type:Publication, On numerical solutions of linear fractional differential equations(2021); Fractional differential equations have excited considerable interest recently, both in pure and applied mathematics. In this paper, we apply Fractional Adams-Bashforth Method (FAB), Fractional Adams-Bashforth-Moulton Method (FABM) and Fractional Multistep Differential Transform Method (FMDTM), for obtaining the numerical solutions of two distinct linear systems of fractional differential equations with fractional derivatives described in the Caputo sense. The numerical results for the three methods are compared with the exact solution for each linear system by using the relative difference between the exact and the approximate solution at each integration point. The results are given both graphically and tabularly, concluding that, aside from occasional non-monotoncity for small time values, all three numerical methods gradually diverge from the exact solution with increasing integration time, and the superiority of each numerical method over the others depends on the particular system under investigation.