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Semi-Analytical Solutions of the Space–Time Fractional Wave Equation for Copper Droplets in Cavitating Flows

Authors

  • Shaukat Iqbal

    School of Systems and Technology, University of Management and Technology, Lahore, 54770, Pakistan
    Author

  • Muhammad Abid

    Department of Mechanical Engineering, Faculty of Engineering, Islamic University of Madinah, Madinah, 42351, Saudi Arabia, KSA
    Author

  • Umair Sabi Ullah

    Department of Computer Science, University of Edinburgh, Glasgow, UK
    Author

  • Hafiz Abdul Wajid

    Department of Electrical Engineering, Faculty of Engineering, Islamic University of Madinah, Madinah, 42351, Saudi Arabia, KSA
    Author

  • Tareq Manzoor

    Energy Research Centre, COMSATS University Islamabad, Lahore Campus, Pakistan
    Author

  • Ayaz Akbar

    Institute of Advanced Interdisciplinary Technology, Shenzhen MSU-BIT University, Shenzhen, China
    Author

  • Sanaulah Manzoor

    School of Computing, Glasgow Caledonian University, Glasgow, UK
    Author

DOI:

https://doi.org/10.22581/0808

Keywords:

Fractional Wave Equation, Adomian Decomposition Method (ADM), Caputo Derivative, Cavitating Flow, Copper Droplets, Semi-analytical Solution

Abstract

In this paper, series solutions of the space–time fractional wave equation modeling copper droplets in cavitating flows are constructed using an extended Adomian Decomposition Method (ADM). The proposed method employs time- and space-fractional derivatives of the Caputo type without linearization or discretization, making it straightforward to implement. Linear and nonlinear wave equation problems are solved to test the accuracy and stability of the method; at integer order (λ = τ = 2), absolute errors on the order of 10−11 (linear case) and 10−4 (nonlinear case) are achieved, respectively. However, the error grows slowly with time in both cases. At fractional orders 1.25, 1.5, and 1.75, the solutions remain smooth and stable.

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References

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Published

2026-10-01

Issue

Vol. 45 No. 4 (2026): October Issue

Section

Articles

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Copyright (c) 2026 Mehran University Research Journal of Engineering and Technology

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How to Cite

Semi-Analytical Solutions of the Space–Time Fractional Wave Equation for Copper Droplets in Cavitating Flows. (2026). Mehran University Research Journal of Engineering and Technology, 45(4), 156-161. https://doi.org/10.22581/0808

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