Some Alternative Solutions to Fractional Models for Modelling Power Law Type Long Memory Behaviours
Jocelyn Sabatier, Christophe Farges, Vincent Tartaglione
Abstract
The paper first describes a process that exhibits a power law-type long memory behaviour: the dynamical behaviour of the heap top of falling granular matter such as sand. Fractional modelling is proposed for this process, and some drawbacks and difficulties associated to fractional models are reviewed and illustrated with the sand pile process. Alternative models that solve the drawbacks and difficulties mentioned while producing power law-type long memory behaviours are presented.
Topics & Concepts
Type (biology)Power lawHeap (data structure)Process (computing)Fractional calculusComputer scienceLawStatistical physicsMathematicsApplied mathematicsAlgorithmPhysicsGeologyPolitical scienceProgramming languageStatisticsPaleontologyFractional Differential Equations SolutionsLandslides and related hazardsDam Engineering and Safety