SOLUTION OF VARIABLE-ORDER NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS USING HAAR WAVELET COLLOCATION TECHNIQUE

Rohul Amin, Hafsa, Fazli Hadi, Mohamed Altanji, Kottakkaran Sooppy Nisar and Wojciech Sumelka
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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

FRACTALS (fractals), 2023, vol. 31, issue 02, 1-9

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.

Keywords: Fractional Calculus; Variable-Order Fractional Differential Equations; Haar Wavelet; Caputo Fractional Derivatives (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400224

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