Applications of Atangana–baleanu fractional operators in modeling Memory-dependent physical and engineering systems
DOI:
https://doi.org/10.29070/8q754d41Keywords:
Atangana–Baleanu operators, memory-dependent systems, anomalous diffusion, fractional circuits, fractional epidemic models, fractional finance, numerical simulationAbstract
Atangana-Baleanu fractional operators, with their non-singular and non-local Mittag-Leffler kernel, represent a powerful tool for modelling physical and engineering systems with memory for hereditary effect and anomalous transport behaviour. The research presented here surveys and develops example applications of the Atangana-Baleanu operator in a spectrum of domains, including physics, engineering, signal processing, biology, epidemiology and financial mathematics. The fractional heat conduction and anomalous diffusion problems were formulated with the AB-Caputo derivative and solved using generalised Laplace transform; the engineering applications were evidenced using the fractional RC circuit and viscoelastic constitutive equations; the signal processing applications were illustrated using fractional filtering and edge-preserving image processing operators; the biological applications were shown via the fractional population growth model and the artificial neural network model; the applications in epidemiology were illustrated by means of the fractional-based SIR model; and the applications in finance were illustrated with the fractional Black-Scholes model and the use of fractional arithmetic on time series sampled from stock market dynamics. Each model includes the governing AB fractional differential equation and either an analytical or semi-analytical solution, along with representative numerical schemes (finite-difference, predictor-corrector and Laplace-transform based) and their stability and error characteristics. A detailed comparative analysis indicates the advantages of the Atangana-Baleanu operator compared to the classical Riemann-Liouville, Caputo and Caputo-Fabrizio operators in all the application areas studied. The analysis also shows that the continuous, non-singular Mittag-Leffler kernel of the Atangana-Baleanu operator provides stable, precise and physically meaningful representations of dynamical systems that display memory dependency.
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