Power-series solutions of fractional-order compartmental models. (English) Zbl 07830983
Summary: Compartmental models based on coupled differential equations of fractional order have been widely employed in the literature for modeling. An abstraction of these models is given by a system with polynomial vector field. We investigate the use of power series for solving generic polynomial differential equations in any dimension, with Caputo fractional derivative. As is well known, power series convert a continuous formulation into a discrete system of difference equations, which are easily solved by recursion. The novelty of this paper is that we rigorously prove that the series converge on a neighborhood of the initial instant, which is an analogue of the Cauchy-Kovalevskaya theorem. Besides, these series are proved to be continuous with respect to the fractional index. For applications, a general-purpose symbolic implementation of truncated power series is developed, and its execution is illustrated for the fractional SIR epidemiological model.
MSC:
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
| 34A08 | Fractional ordinary differential equations |
| 68W30 | Symbolic computation and algebraic computation |
| 92D30 | Epidemiology |
| 39A12 | Discrete version of topics in analysis |
Keywords:
compartmental differential equation system; Caputo fractional derivative; convergent power-series solution; discrete equation; symbolic computation; fractional SIR modelSoftware:
MathematicaReferences:
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