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Solution Of Variable-Order Nonlinear Fractional Differential Equations Using Haar Wavelet Collocation Technique

Author

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  • ROHUL AMIN

    (Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25120, Pakistan)

  • HAFSA

    (Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25120, Pakistan)

  • FAZLI HADI

    (Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25120, Pakistan)

  • MOHAMED ALTANJI

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • KOTTAKKARAN SOOPPY NISAR

    (Department of Mathematics, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Al Kharj 16278, Saudi Arabia4School of Technology, Woxsen University, Hyderabad 502345, Telangana, India)

  • WOJCIECH SUMELKA

    (Institute of Structural Analysis, Poznań University of Technology, Piotrowo 5 Street, Poznań 60-965, Poland)

Abstract

A numerical method for the solution of nonlinear variable-order (VO) fractional differential equations (FDEs) is proposed in this paper. To determine the numerical solution of nonlinear VO FDEs, we used the Haar wavelet collocation method (HWCM) with a combination of Caputo fractional derivatives. For checking the efficiency of the HWCM, some examples are given. The maximum absolute error and mean square root errors of each test problem are computed for a different number of collocation points (CPs) to check the validity and applicability of the presented technique. The comparison of the exact and approximate solution is shown in figures for various numbers of CPs.

Suggested Citation

  • Rohul Amin & Hafsa & Fazli Hadi & Mohamed Altanji & Kottakkaran Sooppy Nisar & Wojciech Sumelka, 2023. "Solution Of Variable-Order Nonlinear Fractional Differential Equations Using Haar Wavelet Collocation Technique," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-9.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:02:n:s0218348x23400224
    DOI: 10.1142/S0218348X23400224
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