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Why Do Big Data and Machine Learning Entail the Fractional Dynamics? [PDF]
Entropy, 2021 Fractional-order calculus is about the differentiation and integration of non-integer orders. Fractional calculus (FC) is based on fractional-order thinking (FOT) and has been shown to help us to understand complex systems better, improve the processing ...
Haoyu Niu, YangQuan Chen, Bruce J. West
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Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo–Fabrizio Derivative [PDF]
Molecules, 2021 Human immunodeficiency virus (HIV) is a life life-threatening and serious infection caused by a virus that attacks CD4+ T-cells, which fight against infections and make a person susceptible to other diseases.
Zahir Shah +4 more
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Mathematics, 2021 General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional ...
Vasily E. Tarasov
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General Non-Markovian Quantum Dynamics
Entropy, 2021 A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus.
Vasily E. Tarasov
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A Generalized Diffusion Equation: Solutions and Anomalous Diffusion
Fluids, 2023 We investigate the solutions of a generalized diffusion-like equation by considering a spatial and time fractional derivative and the presence of non-local terms, which can be related to reaction or adsorption–desorption processes.
Ervin K. Lenzi +4 more
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Anomalous Relaxation and Three-Level System: A Fractional Schrödinger Equation Approach
Quantum Reports, 2023 We investigate a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet.
Ervin K. Lenzi +5 more
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Quantum Reports, 2022 We investigate the solutions of a two-dimensional Schrödinger equation in the presence of geometric constraints, represented by a backbone structure with branches, by taking a position-dependent effective mass for each direction into account.
Ervin K. Lenzi +3 more
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Quantum Maps with Memory from Generalized Lindblad Equation
Entropy, 2021 In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation
Vasily E. Tarasov
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Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches
Mathematics, 2023 We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and the other considers the extension of the concept of entropy, i.e., the Tsallis statistics.
Ervin Kaminski Lenzi +2 more
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Fractal and Fractional, 2023 Infectious diseases can have a significant economic impact, both in terms of healthcare costs and lost productivity. This can be particularly significant in developing countries, where infectious diseases are more prevalent, and healthcare systems may be
Sultan Alyobi, Rashid Jan
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