Application of the Euler and Runge-Kutta generalized methods for FDE and symbolic packages in the analysis of some fractional attractors

DOI10.1515/ijnsns-2018-0248OpenAlexW2981732193WikidataQ114053000 ScholiaQ114053000MaRDI QIDQ2180958

Constantin Milici, Gheorghe Drăgănescu, José António Tenreiro Machado

Publication date: 18 May 2020

Published in: International Journal of Nonlinear Sciences and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ijnsns-2018-0248

zbMATH Keywords

stabilityRunge-Kutta methodEuler methodfractional differential equationsLyapunov exponentCaputo derivativeLorenz fractional attractorTaylor generalized formula

Mathematics Subject Classification ID

Numerical analysis (65-XX) Ordinary differential equations (34-XX)

Related Items (1)

Generalized forms of fractional Euler and Runge-Kutta methods using non-uniform grid

Uses Software

• Maple
• Mathematica
• RODAS
• FracPECE

Cites Work

• A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Picard's iterative method for Caputo fractional differential equations with numerical results
• Numerical solution of fractional differential equations: a survey and a software tutorial
• The numerical solution of differential-algebraic systems by Runge-Kutta methods
• On the fractional Cornu spirals
• A review of definitions of fractional derivatives and other operators
• Numerical Methods
• Solving Ordinary Differential Equations I
• Stability, Instability and Chaos
• Deterministic Nonperiodic Flow
• Fractional differentiation matrices with applications
• Numerical Methods for Ordinary Differential Equations
• Liapunov functions and stability in control theory
• Analysis of fractional differential equations
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