Approximation of Some Nonlinear Fractional Order BVPs by Weighted Residual Methods

Abstract

To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such as Galerkin, Least Square, and Collocation for the efficient numerical solution of nonlinear two-point boundary value problems. Some nonlinear cases are examined for observing the maximum absolute errors by the considered methods, demonstrating the accuracy and reliability of the present technique using the modified Legendre and modified Bernoulli polynomials as weight functions. The mathematical formulations and computational algorithms are more straightforward and uncomplicated to understand. Absolute errors and the graphical representation reflect that our method is more accurate and reliable.