Universality in Systems with Power-Law Memory and Fractional Dynamics (Q4609622)

scientific article; zbMATH DE number 6856098

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English	Universality in Systems with Power-Law Memory and Fractional Dynamics	scientific article; zbMATH DE number 6856098

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instance of

scholarly article

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title

Universality in Systems with Power-Law Memory and Fractional Dynamics (English)

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zbMATH Open document ID

1386.37082

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DOI

10.1007/978-3-319-68109-2_8

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author

Mark Edelman

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published in

Understanding Complex Systems

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publication date

5 April 2018

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full work available at URL

https://arxiv.org/abs/1709.00093

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Mathematics Subject Classification ID

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power-law memory

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transition to chaos

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MaRDI profile type

MaRDI publication profile

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Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems

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Nabla discrete fractional calculus and nabla inequalities

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Initial value problems in discrete fractional calculus

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Discrete fractional calculus with the nabla operator

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Stability analysis of Caputo-like discrete fractional systems

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Discrete-time fractional variational problems

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Necessary optimality conditions for fractional difference problems of the calculus of variations

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Existence results for nonlinear fractional difference equation

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Q3992989

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Fractional standard map: Riemann-Liouville vs. Caputo

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Fractional Maps and Fractional Attractors. Part I: α-Families of Maps

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Universal fractional map and cascade of bifurcations type attractors

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Caputo standard α-family of maps: Fractional difference vs. fractional

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Fractional Maps and Fractional Attractors. Part II: Fractional Difference Caputo α- Families of Maps

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On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations

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Fractional standard map

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New Types of Solutions of Non-linear Fractional Differential Equations

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Fractional h-difference equations arising from the calculus of variations

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A formulation of Noether's theorem for fractional problems of the calculus of variations

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On a New Definition of the Fractional Difference

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Nonlinear differential equations of fractional order in the space of integrable functions.

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Q4521165

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Q5699297

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Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability

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Stability properties for generalized fractional differential systems

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Simple mathematical models with very complicated dynamics

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Q3468036

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Overview of Fractional h-difference Operators

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Constrained Controllability of h-Difference Linear Systems with Two Fractional Orders

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Stability of nonlinear h-difference systems with n fractional orders

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Fractional-order nonlinear systems. Modeling, analysis and simulation

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Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications

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Stability of fractional order systems

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Q3141895

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Long-term memory contribution as applied to the motion of discrete dynamical systems

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Differential equations with fractional derivative and universal map with memory

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Discrete map with memory from fractional differential equation of arbitrary positive order

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Fractional equations of kicked systems and discrete maps

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Discrete chaos in fractional sine and standard maps

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Q5710170

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Chaotic and pseudochaotic attractors of perturbed fractional oscillator

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mardi Publication:4609622