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Galerkin’s method to solve a fractional time-delayed jerk oscillator

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Abstract

An immediate analytic solution for the time-delayed fractional linear jerk oscillator is derived in the present study. The currently used method adheres to basic, easily implementable criteria. This proposed approach is based on transforming the time-delayed fractional oscillator to an equivalent oscillator with ordinary derivatives, which makes the solution procedure simple. The conversion process steps to an equivalent ordinary differential oscillator are displayed. Galerkin’s method is used to derive the jerk frequency. The good match between the analytic and numerical outcomes shows that the equivalent linearized mechanism leads to finding a satisfying and accurate solution. Stability discussion is conducted analytically and numerically.

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Acknowledgements

The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project Number (PNURSP2023R17), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

    Yusry O. El-Dib & Nasser S. Elgazery

  2. Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11681, Saudi Arabia

    Haifa A. Alyousef

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  1. Yusry O. El-Dib
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El-Dib, Y.O., Elgazery, N.S. & Alyousef, H.A. Galerkin’s method to solve a fractional time-delayed jerk oscillator. Arch Appl Mech 93, 3597–3607 (2023). https://doi.org/10.1007/s00419-023-02455-8

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