This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n + 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended approach is applicable and accurate for solving such kinds of problems.
ABSTRACT
The research aim is to determine the relation between governmental consumption expenditure (GCE) & GDP in Iraq for the period 1981-2006.
The research has determined the scale of optimization for (GCE) & try to know the extent productivity of this expenditure and using the long run &short run model to test .The results clarify the following
1-The marginal productivity for the (GCE) is positive so it is productive.
2-The (GCE) in Iraq is too high because the marginal productivity for the expenditure less than 1.
3- The (GCE) percentage to GNP is
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