Stability Analysis and Solutions of a Fractional-Order Model for the Glucose-Insulin Homeostasis in Rats
The main objectives of this works are to introduce a fractional order model of the glucose-insulin homeostasis in rats, to establish conditions for which an equilibrium point of the model is asymptotically stable, and to apply standard methods to solve the model for solutions. The exact solutions of the fractional-order model are derived using the Laplace transform. In particular, we apply the Laplace-Adomian- Padé method (LAPM), which is based on the Laplace-Adomian decomposition method (LADM), and the Adams-Bashforth-Moulton type predictor-corrector scheme to solve the model for analytical and numerical solutions, respectively. Moreover, the obtained exact solutions of this fractional-order model are employed to numerically and graphically compare with the results obtained using the proposed two methods. The LAPM and the predictor-corrector scheme can also be applied simply and efficiently to other fractional-order differential systems arising in engineering and applied mathematics problems.
KeywordsAsymptotic stability Adams-Bashforth-Moulton predictor-corrector scheme Caputo fractional-order derivative Commensurate fractional-order model Exact solutions Laplace-Adomian decomposition method Padé approximation
This research is supported by the Department of Mathematics, King Mongkut’s University of Technology North Bangkok, Thailand and the Centre of Excellence in Mathematics, the Commission on Higher Educaton, Thailand.
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