Numerical solution of multi-order fractional differential equations using orthogonal polynomial basis

Abstract

This paper presents the solution of multi-order fractional differential equations using a constructed orthogonal polynomial as the basis function. An approximate solution was assumed and substituted into a general class of multi-order fractional differential equations of the form Dα1y(x)+Dα2y(x)+⋯+Dαny(x)=f(x) With initial conditions y(0)=μ Where Dα are parameters denoting the fractional order derivatives in Caputo sense. The resulting equation was collocated equally spaced interior points. The unknown constants in the assumed approximate solution were obtained using Gaussian elimination method. Some numerical examples are presented to illustrate the method