In this work we make use of the Reimann-Liouville definition of fractional derivative to define the fractional order integro-differential equations without and with delay. Also we present and modify some approaches to get the solution of the fractional order integro-differential equation with and without delay; where we present the expansion(collocation) method as approximate method; then we give the variational fonnulation for the fractional order integro-differential equation with and without delay and we solve them by variational approach making use of Ritz method. Finally we gave some applications of the fractional differential operator in different some branches. In our work we make use of the Matlab v.6.1 software and the Basic programming language to solve the discussed examples.