A COMPUTATIONAL ALGORITHM FOR THE NUMERICAL SOLUTION OF NONLINEAR FRACTIONAL INTEGRAL EQUATIONS

Rohul Amin (), Norazak Senu (), Muhammad Bilal Hafeez (), Noreen Izza Arshad (), Ali Ahmadian, Soheil Salahshour and Wojciech Sumelka ()
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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

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-8

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.

Keywords: NFIEs; Uniqueness and Existence; HWCT; CPs (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22400308

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DOI: 10.1142/S0218348X22400308

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