Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms. (July 2020)

• Record Type: Journal Article
• Authors: Khater, Mostafa M.A.; Attia, Raghda A.M.; Abdel-Aty, Abdel-Haleem; Alharbi, W.; Lu, Dianchen
• Is Part Of: Chaos, solitons and fractals. Volume 136(2020)
• Publication Date: 2020-07
• Subjects: The nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation -- ABR fractional operator -- Generalized Sinh–Gorden expansion method -- B-spline schemes; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.109824
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this paper, an analytical scheme [the generalized Sinh–Gordon equation method) with a new fractional operator ( ABR fractional operator] is employed to find novel computational solutions of the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation. These solutions are used to evaluate the initial and boundary conditions under the numerical scheme (B-spline schemes) to get the numerical solutions of the same model. This equation describes the behavior of genetic models in the increase of microorganisms. Usually, it is used as a biological model to investigate the microbiological densities in bacteria cells as a result of diffusion mechanisms in terms of space–time. Some novel computational solutions are obtained, and the accuracy of them is investigated by calculating the absolute value of error between the obtained computational and numerical solutions. The comparison between the distinct types of obtained solutions is shown by calculating the absolute value of error.