ABSTRACT
This chapter proposes a new wavelet method based on the Hermite wavelet expansion together with operational matrices of fractional integration and derivative of wavelet functions to solve a time-fractional modified Fornberg–Whitham equation. With a view to exhibit the capabilities of the proposed wavelet method, the chapter employs the method to deal with fractional modified Fornberg–Whitham equations and fractional order coupled Jaulent–Miodek equations. The approximate solutions attained via the Hermite wavelet technique were compared with exact solutions and those derived by using optimal homotopy asymptotic method (OHAM) in the case of fractional order. The proposed numerical algorithm implemented in numerical experiment is easy to implement, and it does not depend upon the mesh of discretized time and space. To exhibit the effectiveness and accuracy of the proposed numerical scheme, the chapter considers the time-fractional modified Fornberg–Whitham equation. To demonstrate the accuracy and efficiency of the proposed numerical technique, it also considers the time-fractional coupled Jaulent–Miodek equation.
