In this paper, numerical solution of initial and boundary value problems for nonlinear fractional differential equations is considered by pseudospectral method. In order to avoid solving systems of nonlinear equations resulting from the method, the residual function of the problem is constructed, as well as a suggested unconstrained optimization model solved by PSOGSA algorithm. Furthermore, the research inspects and discusses the spectral accuracy of Chebyshev polynomials in the approximation theory. The following scheme is tested for a number of prominent examples, and the obtained results demonstrate the accuracy and efficiency of the proposed method.
Delpasand, R.; Hosseini, M. M.; and Maalek Ghaini, F. M.
A new hybrid method for solving nonlinear fractional differential equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 12,
2, Article 14.
Available at: https://digitalcommons.pvamu.edu/aam/vol12/iss2/14