Hybrid time-space dynamical systems of growth bacteria with applications in segmentation

•We establish the existence and uniqueness results of time-space FDE of growing bacteria.•We introduce the numerical solution for this equation using a homotopy method.•We study the Ulam stability of it utilizing fractional inequalities.•We apply the above result to segment images of bacteria. A bio...

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Vydáno v:Mathematical biosciences Ročník 292; s. 10 - 17
Hlavní autoři: Ibrahim, Rabha W., Nashine, Hemant K., Kamaruddin, Norshaliza
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States Elsevier Inc 01.10.2017
Elsevier Science Ltd
Témata:
Analytic function
Approximation
Bacteria
Bacteria - growth & development
Cellular communication
Communication networks
Communications systems
Control systems
Data processing
Dynamical systems
Fractional calculus
Fractional differential equations
Fractional differential operators
Homotopy method
Hybrid systems
Image processing
Image segmentation
Models, Biological
Molecular biology
Molecular chains
Operators
Perturbation methods
Signal processing
Spatio-Temporal Analysis
Ulam stability
Unit disk
Univalent function
Homotopy method
Fractional differential equations
Unit disk
34A12
Fractional differential operators
Univalent function
Analytic function
Ulam stability
Fractional calculus
34A08
ISSN:0025-5564, 1879-3134, 1879-3134
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Shrnutí:•We establish the existence and uniqueness results of time-space FDE of growing bacteria.•We introduce the numerical solution for this equation using a homotopy method.•We study the Ulam stability of it utilizing fractional inequalities.•We apply the above result to segment images of bacteria. A biological dynamic system carries engineering properties such as control systems and signal processing (or image processing) addicted to molecular biology at the level of bio-molecular communication networks. Dynamical system features and signal reply functions of cellular signaling pathways are some of the main topics in biological dynamic systems (for example the biological segmentation). In the present paper, we introduce new generalized hybrid time-space dynamical systems of growing bacteria. We impose the approximate analytic solution for the system. The generalization adapted the concepts of the Riemann–Liouville fractional operators for time and the Srivastava–Owa fractional operators for space. Moreover, we introduce a numerical perturbation method of two operators to obtain the approximate solutions. We establish the existence and uniqueness results and impose some applications in the sequel. Moreover, we study the Ulam stability and apply these stable solutions to improve the segmentation of a class of growing bacteria.
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ISSN:0025-5564
1879-3134
1879-3134
DOI:10.1016/j.mbs.2017.07.007