A Fast and Accurate Genocchi Wavelet Approach for Multi-Term Fractional Differential Equations

In this article, a hybrid numerical scheme based on Genocchi wavelet is proposed to solve multi-term fractional differential equations (FDEs). Using function approximation and operational matrix of integration, these multi-term FDEs are converted into system of algebraic equations which is solved by Newton-Raphson method. Test examples are examined such that large class of multi-term FDEs can be covered. CPU time and Comparison with the existing methods like Haar wavelet collocation method, Chebyshev polynomial method, fractional backward difference method, Chelyskhov polynomial collocation method and generalized Chebyshev polynomial method shows that our proposed Genocchi method is computationally efficient and produce better results. Error has been shown graphically for these different multi-term FDEs. Moreover, only a small number of basis points is needed to obtain a satisfactory result.