New Types of Solutions of Non-linear Fractional Differential Equations

Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 229)

Abstract

Using the Riemann-Liouville and Caputo Fractional Standard Maps (FSM) and the Fractional Dissipative Standard Map (FDSM) as examples, we investigate types of solutions of non-linear fractional differential equations. They include periodic sinks, attracting slow diverging trajectories (ASDT), attracting accelerator mode trajectories (AMT), chaotic attractors, and cascade of bifurcations type trajectories (CBTT). New features discovered include attractors which overlap, trajectories which intersect, and CBTTs.

Keywords

Discrete map attractor fractional dynamical system map with memory stability. 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Stern College for Women at Yeshiva UniversityNew YorkUSA

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