Piecewise derivatives versus short memory concept: analysis and application.
Copyright policy )Piecewise derivatives versus short memory concept: analysis and application.
We have provided a detailed analysis to show the fundamental difference between the concept of short memory and piecewise differential and integral operators. While the concept of short memory leads to different long tails in different intervals of time or space as a result of a power law with different fractional orders, the concept of piecewise helps to depict crossover behaviors of different patterns. We presented some examples with different numerical simulations. In some cases piecewise models led to transitional behavior from deterministic to stochastic, this is indeed the reason why this concept was introduced.
- University of the Free State South Africa
- Siirt University Turkey
- China Medical University Hospital Taiwan
- China Medical University Taiwan
crossover behaviors, chaos, Fractional ordinary differential equations, Discontinuous ordinary differential equations, Piecewise Calculus, piecewise calculus, Short Memory Concept, Fractional derivatives and integrals, short memory concept, Qualitative investigation and simulation of ordinary differential equation models, QA1-939, epidemiology, TP248.13-248.65, Mathematics, Biotechnology
crossover behaviors, chaos, Fractional ordinary differential equations, Discontinuous ordinary differential equations, Piecewise Calculus, piecewise calculus, Short Memory Concept, Fractional derivatives and integrals, short memory concept, Qualitative investigation and simulation of ordinary differential equation models, QA1-939, epidemiology, TP248.13-248.65, Mathematics, Biotechnology
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!