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A Computational Algorithm For The Numerical Solution Of Nonlinear Fractional Integral Equations

Author

Listed:
  • ROHUL AMIN

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

  • NORAZAK SENU

    (Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM, Selangor, Malaysia)

  • MUHAMMAD BILAL HAFEEZ

    (Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5 Street, 60-969 Poznan, Poland)

  • NOREEN IZZA ARSHAD

    (Department of Computer and Information Sciences, Universiti Teknologi Petronas, 32610, Bandar Seri Iskandar, Perak, Malaysia)

  • ALI AHMADIAN

    (Institute of IR 4.0, The National University of Malaysia, Bangi, 43600 UKM, Selangor, Malaysia6Department of Mathematics, Near East University, Nicosia TRNC, Mersin 10, Turkey)

  • SOHEIL SALAHSHOUR

    (Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey)

  • WOJCIECH SUMELKA

    (Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5 Street, 60-969 Poznan, Poland)

Abstract

In this paper, we develop a numerical method for the solution of nonlinear fractional integral equations (NFIEs) based on Haar wavelet collocation technique (HWCT). Under certain conditions, we also prove the uniqueness and existence as well as Hyers–Ulam (HU) stability of the solution. With the help of the mentioned technique, the considered problem is transformed to a system of algebraic equations which is then solved for the required results by using Broyden algorithm. To check the validation and convergence of the proposed technique, some examples are given. For different number of collocation points (CPs), maximum absolute and mean square root errors are computed. The results show that for solving these equations, the HWCT is effective. The convergence rate is also measured for different CPs, which is nearly equal to 2.

Suggested Citation

  • Rohul Amin & Norazak Senu & Muhammad Bilal Hafeez & Noreen Izza Arshad & Ali Ahmadian & Soheil Salahshour & Wojciech Sumelka, 2022. "A Computational Algorithm For The Numerical Solution Of Nonlinear Fractional Integral Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-8, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22400308
    DOI: 10.1142/S0218348X22400308
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