Gegenbauer Wavelet Collocation Method for the Fractional Unsteady Squeezing Flow of Casson Fluid

Gegenbauer (Ultraspherical) wavelets operational matrices play a main role in the approximate solution of ordinary and partial differential equations. This study presents operational matrices of Caputo fractional derivatives of Gegenbauer wavelets for the first time. The proposed method is based on the approximation by the truncated Gegenbauer wavelet series. Components of operational matrices of Caputo fractional derivatives have been obtained as some series. The present method has transformed the differential equation into an algebraic equation system by using the collocation points. The proposed Gegenbauer wavelet collocation method has been applied to the fractional unsteady squeezing flow of Casson fluid problem using quasilinearization technique to show the feasibility and accuracy of the present method. The computed results well match the results given in the literature. These calculations demonstrate that the accuracy of the Gegenbauer wavelet collocation method is quite good even for a small number of grid points.