In this paper, normalized Bernstein wavelets are presented. Next, the fractional order integration and Bernstein wavelets operational matrices of integration are derived and finally are used for solving fractional partial differential equations. The operational matrices merged with the collocation method are used in order to convert fractional problems to a number of algebraic equations. In the suggested method the boundary conditions are automatically taken into consideration. An assessment of the error of function approximation based on the normalized Bernstein wavelet is also presented. Some numerical instances are given to manifest the versatility and applicability of the suggested method. Founded numerical results are correlated with the best reported results in the literature and the analytical solutions in order to prove the accuracy and applicability of the suggested method.
Entezari, Mahsa; Abbasbandy, Saeid; and Babolian, Esmail
Numerical Solution of Fractional Partial Differential Equations with Normalized Bernstein Wavelet Method,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 14,
2, Article 17.
Available at: https://digitalcommons.pvamu.edu/aam/vol14/iss2/17