Journal Article10.1007/S00366-020-01170-0
Two efficient numerical schemes for simulating dynamical systems and capturing chaotic behaviors with Mittag–Leffler memory
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TL;DR: Two accurate iterative methods for solving fractional differential equations with power law and Mittag–Leffler kernel based on trapezoidal product-integration rule and Lagrange interpolations are considered.
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Abstract: In this paper, we consider two accurate iterative methods for solving fractional differential equations with power law and Mittag–Leffler kernel. We focused our attention on the stage-structured prey–predator model and several chaotic attractors of type Newton–Leipnik, Rabinovich–Fabrikant, Dadras, Aizawa, Thomas’ and 4 wings. The first algorithm is based on the trapezoidal product-integration rule, and the second one is based on Lagrange interpolations. The results obtained show that both numerical methods are very efficient and provide precise and outstanding results to determine approximate numerical solutions of fractional differential equations with non-local singular kernels.
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References
•Book
Fractional Integrals and Derivatives: Theory and Applications
Stefan Samko,Anatoly A. Kilbas,O. I. Marichev +2 more
- 08 Dec 1993
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Analysis of Fractional Differential Equations
Kai Diethelm,Neville J. Ford +1 more
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
3.6K
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model
Abdon Atangana,Dumitru Baleanu +1 more
TL;DR: In this article, a new fractional derivative with non-local and no-singular kernel was proposed and applied to solve the fractional heat transfer model, and some useful properties of the new derivative were presented.
A new Definition of Fractional Derivative without Singular Kernel
Michele Caputo,Mauro Fabrizio +1 more
- 01 Jan 2015
TL;DR: In this article, the authors present a new definition of fractional derivative with a smooth kernel, which takes on two different representations for the temporal and spatial variable, for which it is more convenient to work with the Fourier transform.
2.7K
•Book
A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations
Kai Diethelm,Neville J. Ford,Alan D. Freed +2 more
- 07 Aug 2013
TL;DR: In this paper, an Adams-type predictor-corrector method for the numerical solution of fractional differential equations is discussed, which may be used both for linear and nonlinear problems, and it may be extended tomulti-term equations (involving more than one differential operator) too.
1.8K