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An Approximate Method for Solving a Vibration Equation Involving Fractional Derivatives

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Acoustics and Vibration of Mechanical Structures—AVMS-2017

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 198))

Abstract

The response of one-degree-of-freedom systems with fractional distributed-order damping is studied. The dynamics of such systems constitutes the problem of the fractional distributed-order oscillator. This paper presents a new numerical method for solving this fractional distributed order oscillator. The method is based on using fractional Taylor vector approximation. The operational matrix of the fractional integration for fractional Taylor vector is given and is utilized to reduce the solution of the fractional distributed order oscillator to a system of algebraic equations. An illustrative example is included to demonstrate the validity and applicability of this technique.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Mississippi State University, Starkville, MS, 39762, USA

    Mohsen Razzaghi

Authors
  1. Mohsen Razzaghi
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Correspondence to Mohsen Razzaghi .

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Editors and Affiliations

  1. Department of Mechanics and Strength of Materials, University Politehnica TimiĹźoara, TimiĹźoara, Romania

    Nicolae Herisanu

  2. Centre for Fundamental and Advanced Technical Research, Romanian Academy, Branch of TimiĹźoara, TimiĹźoara, Romania

    Vasile Marinca

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Razzaghi, M. (2018). An Approximate Method for Solving a Vibration Equation Involving Fractional Derivatives. In: Herisanu, N., Marinca, V. (eds) Acoustics and Vibration of Mechanical Structures—AVMS-2017. Springer Proceedings in Physics, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-319-69823-6_2

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