Collocation method with convergence for generalized fractional integro-differential equations

In this paper, we study a numerical approach for some class of generalized fractional integro-differential equations (GFIDEs) defined in terms of the B-operators presented recently. We develop collocation method for linear and nonlinear forms of GFIDEs. The numerical approach uses the idea of collocation methods for solving integral equations. Legendre polynomials are used to approximate the solution in finite dimensional space with convergence analysis. The obtained approximate solution recovers the solution of the fractional integro-differential equation (FIDE) defined using Caputo derivatives in a special case. FIDEs containing convolution type kernels appear in diverse area of science and engineering applications; therefore, some test examples varying the kernel in the B-operator are considered to perform the numerical investigations. The numerical results validate the presented scheme and provide good accuracy using few Legendre basis functions.