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Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives
- Source :
- Chaos, Solitons & Fractals. 127:146-157
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- This paper considers mathematical analysis and numerical treatment for fractional reaction-diffusion system. In the model, the first-order time derivatives are modelled with the fractional cases of both the Atangana-Baleanu and Caputo-Fabrizio derivatives whose formulations are based on the notable Mittag-Leffler kernel. The main system is examined for stability to ensure the right choice of parameters when numerically simulating the full model. The novel Adam-Bashforth numerical scheme is employed for the approximation of these operators. Applicability and suitability of the techniques introduced in this work is justified via the evolution of the species in one and two dimensions. The results obtained show that modelling with fractional derivative can give rise to some Turing patterns.
- Subjects :
- Work (thermodynamics)
Computer simulation
General Mathematics
Applied Mathematics
Frame (networking)
General Physics and Astronomy
Statistical and Nonlinear Physics
01 natural sciences
Stability (probability)
010305 fluids & plasmas
Fractional calculus
Modeling and simulation
Kernel (image processing)
Scheme (mathematics)
0103 physical sciences
Applied mathematics
010301 acoustics
Mathematics
Subjects
Details
- ISSN :
- 09600779
- Volume :
- 127
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi...........1a1225a892c0b3558260cd0fe7a6f64b