Identification of fractional water transport model with \(\psi \)-Caputo derivatives using particle swarm optimization algorithm. (English) Zbl 1474.35639
Summary: The paper studies a \(\psi \)-Caputo space-time-fractional moisture transport model stated in terms of water head. We consider a functional parameter of \(\psi \)-Caputo derivatives in power and sigmoid forms and use particle swarm optimization algorithm to identify model’s parameters. Input data for the identification were acquired on the irrigated field in the South of Ukraine within one irrigation cycle. Direct problems were solved using a finite-difference scheme. In these conditions, application of a fractional model with the classic Caputo derivative allowed more than \(\sim 2\)-times lowering of average absolute error compared to the integer-order model. The usage of functional parameter in power form allowed up to 19% accuracy enhancement compared to the classic Caputo derivative while the usage of sigmoid function up to 2.6-times lowers the error. Such behaviour remains when predicting soil moisture dynamics within the following irrigation cycles.
MSC:
| 35R11 | Fractional partial differential equations |
| 90C59 | Approximation methods and heuristics in mathematical programming |
Keywords:
moisture transport; fractional differential equation; parameters identification; \( \psi \)-Caputo derivative; sigmoid function; particle swarm optimizationReferences:
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