Exponentially Fitted Collocation Method for Solving Singular Multi-Fractional Integro-Differential Equations.

Abstract

This work considered the construction of canonical polynomials and used as basis functions for the approximation of singular multi-order fractional integro-differential equations. The idea is that the singular multi-order problem is slightly perturbed with shifted Chebyshev polynomials, and the resulting equation is collocated at equally spaced interior points. The conditions are exponentially fitted with one tau-parameter along with the unknown constants. This results into a system of linear algebraic equations which are then solved using Gaussian elimination method to obtain the unknown parameters involved. Some examples are solved to demonstrate the effectiveness of the method.