A new collocation approach for a numerical treatment of multi order fractional differential equations

This paper discusses the numerical solution of multi-order fractional differential equations by Exponentially fitted collocation method using two basis functions, namely, the Bernoulli polynomial and shifted Legendre polynomials. The fractional derivatives are expressed in the Caputo sense. The assumed solution is substituted into the problem considered an then manipulated. The resulting equation is then collocated at equidistant points. Hence, reducing it to an algebraic linear system of equations which are then solved using Maple 18 to obtain the unknown constants. Three numerical examples are considered to test the applicability and accuracy of the method. The results obtained show that the trial solution with Bernoulli polynomial performed well than shifted Legendre polynomials in the problem considered.