Capturing Nonlocal Effects in Fractional Dynamics: Riesz Derivatives as a New Frontier in Modeling Complex Diffusion and Pattern Formation
Sign Up to like & getrecommendations! Published in 2025 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.70120
Abstract: This work addresses the numerical solution of fractional time‐dependent partial differential equations (FTPDEs) that involve the Riesz fractional derivative in space. Motivated by the effectiveness of space‐fractional operators in modeling anomalous diffusion and dispersion phenomena… read more here.
Keywords: fractional dynamics; diffusion; pattern formation; diffusion pattern ... See more keywords
Fractional dynamics of an erbium-doped fiber laser model
Sign Up to like & getrecommendations! Published in 2019 at "Optical and Quantum Electronics"
DOI: 10.1007/s11082-019-2033-3
Abstract: In this paper we investigate the model of the time-fractional dynamics of an erbium-doped fiber laser model (TFDEFL) with Liouville–Caputo (LC), Caputo–Fabrizio–Caputo (CFC) and Atangana–Baleanu–Caputo (ABC) time-fractional derivatives. We employ the homotopy analysis transform method… read more here.
Keywords: dynamics erbium; doped fiber; erbium doped; model ... See more keywords
The fractional dynamics of quantum systems
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DOI: 10.1016/j.aop.2018.03.017
Abstract: Abstract The fractional dynamic process of a quantum system is a novel and complicated problem. The establishment of a fractional dynamic model is a significant attempt that is expected to reveal the mechanism of fractional… read more here.
Keywords: dynamics quantum; quantum systems; system; time fractional ... See more keywords
Fractional Dynamics of PMU Data
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DOI: 10.1109/tsg.2020.3044903
Abstract: Novel dynamics are emerging in the power system due to the new Smart Grid (SG) environment. The high sampling rate of the Phasor Measurement Units (PMUs) enables them to capture the dynamic fluctuations in the… read more here.
Keywords: pmu data; fractional dynamics; dynamics pmu; power system ... See more keywords
Fractional Dynamics of Cancer Cells and the Future of Research in Biomedicine
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DOI: 10.11648/j.crj.20180601.13
Abstract: Following our previous works on fractional biophysical issues such as fractional dynamics of protein folding process and fractional dynamics of cancer cells and their branching processes, in this work we further develop these issues and… read more here.
Keywords: research; biomedicine; cancer cells; dynamics cancer ... See more keywords
Fractional Dynamics of a Measles Epidemic Model
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DOI: 10.3390/axioms11080363
Abstract: In this work, we replaced the integer derivative with Caputo derivative to model the transmission dynamics of measles in an epidemic situation. We began by recalling some results on the local and global stability of… read more here.
Keywords: measles epidemic; dynamics measles; epidemic model; model fractional ... See more keywords
Complex and Fractional Dynamics
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DOI: 10.3390/e19020062
Abstract: Complex systems (CS) are pervasive in many areas, namely financial markets; highway transportation; telecommunication networks; world and country economies; social networks; immunological systems; living organisms; computational systems; and electrical and mechanical structures. CS are often… read more here.
Keywords: complex fractional; fractional dynamics;