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A numerical scheme based on Gegenbauer wavelets for solving a class of relaxation–oscillation equations of fractional order

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Abstract

Owing to increasing applications of the fractional relaxation–oscillation equations across various scientific endeavours, a considerable amount of attention has been paid for solving these equations. Our endeavour is to develop an elegant numerical scheme based on Gegenbauer wavelets for solving the fractional-order relaxation–oscillation equations. To facilitate the narrative, the Gegenbauer wavelets are presented and the corresponding operational matrix of fractional-order integration is constructed via the block pulse functions. The prime features of the Gegenbauer wavelets and block pulse functions are then utilized to reduce the system at hand into a set of algebraic equations, solved by means of Newton method. The efficiency and accuracy of the proposed numerical scheme are demonstrated via several illustrative examples.

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Authors and Affiliations

  1. Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawasir, 11991, Saudi Arabia

    Kottakkaran Sooppy Nisar

  2. Department of Mathematics, University of Kashmir, South Campus, Anantnag, Jammu and Kashmir, 192101, India

    Firdous A. Shah

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Nisar, K.S., Shah, F.A. A numerical scheme based on Gegenbauer wavelets for solving a class of relaxation–oscillation equations of fractional order. Math Sci 17, 233–245 (2023). https://doi.org/10.1007/s40096-022-00465-1

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