Exponential Enclosures for the Verified Simulation of Fractional-Order Differential Equations

Fractional-order differential equations are powerful tools for the representation of dynamic systems that exhibit long-term memory effects. The verified simulation such system models with help interval allows computation guaranteed enclosures domains reachable pseudo states over a certain finite time horizon. In previous work author, an iteration scheme—derived on basis Picard iteration—was published makes use Mittag-Leffler functions to determine pseudo-state enclosures. this paper, corresponding is generalized toward exponential during evaluation scheme. Such well-known from solution integer-order sets equations. aim demonstrate instead pure box-type does not only improve tightness computed but also reduces required computational effort. These statements demonstrated close-to-life model charging/discharging dynamics Lithium-ion batteries.