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Maxey–Riley equation: newer perspective

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Abstract

Non-integer-order derivatives have proven useful while modelling natural systems involving memory effects. In this article, we analyse the Maxey–Riley (M–R) equation that models the motion of a small particle in a non-uniform flow field. Fractional derivative arises naturally as a history term. We study the M–R equation in terms of fractional differential equations, a subject very well studied in recent times. This approach helps in gaining a deeper understanding of the underlying phenomenon. We observe solution curves having self-intersections, which is a novel feature of fractional-order dynamics.

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Data sharing does not apply to this article as no datasets were generated or analysed during the current study.

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Basic Mathematica commands were used to plot the solutions and can be provided by the corresponding author upon request.

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  1. Abhiram Hegade, Varsha Daftardar-Gejji, and Sachin Bhalekar have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Statistics, University of Hyderabad, Hyderabad, Telangana, 500046, India

    Abhiram Hegade & Sachin Bhalekar

  2. Department of Scientific Computing, Modeling and Simulation, Savitribai Phule Pune University, Pune, Maharashtra, 411007, India

    Varsha Daftardar-Gejji

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  1. Abhiram Hegade
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  2. Varsha Daftardar-Gejji
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  3. Sachin Bhalekar
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Correspondence to Abhiram Hegade.

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Hegade, A., Daftardar-Gejji, V. & Bhalekar, S. Maxey–Riley equation: newer perspective. Int. J. Dynam. Control 12, 85–97 (2024). https://doi.org/10.1007/s40435-023-01268-5

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  • DOI: https://doi.org/10.1007/s40435-023-01268-5

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