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

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.