The aim of the present study was the histological evaluation of Enamel matrix derivative (EMD) effectiveness for regeneration of periodontal defects. EMD activates cementum synthesis, PDL and bone during the maturation stage of follicole. In this research, EMD was used in surgical defects of premolar teeth in four adult sheep. Muccoperiosteal flap was reflected in buccal site of teeth. The buccal bone plate was removed from mesial to distal in 4 mm depth. After eliminating the cementum by bur and its etching, EMD was applied on exposed dentine and flap was sutured. In opposite sites of those teeth (control sites) the same process was performed without etching. After 100 days, sheep were sacrificed and histological study through light microscopic was performed on black sections of operation sites. The results showed that in test sites, regeneration of cementum and bone was 62/5% and 42/5-50% respectively. But in control sites regeneration of cementum and bone was 37.5% and 32/5-42/5% respectively. Also the migration of junctional epithelium in control sites was 8-10% more than test sites. The important point is that in test sites, cementum was completely attached to undermining dentine. But, in control sites, the gap between cementum and dentine was visible. As a result, this study suggests that EMD promotes periodontal regeneration, and EMD application is a successful achievement in regenerative periodontal therapy.

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and Operational matrix of product based on the Bernstein basis. Then, we get the Bernstein Operational matrix for the Jumarie’s modified Riemann-Liouville fractional derivative, which has not been undertaken before. By using the function approximations based on the Bernstein basis and mentioned Operational matrices, the optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative is reduced to a system of algebraic equations that easily solvable by Newton’s iteration method. We apply the proposed method for solving two examples. The numerical results show that present method is simple in implementation and the approximate solutions are in high accuracy. Some comparisons with other method guarantee that the results are reasonable. Also, the obtained solutions approach to classical solutions as the order of the fractional derivatives approach to 1, as expected.

In this paper, we apply the extended triangular Operational matrices of fractional order to solve the fractional voltrra model for population growth of a species in a closed system. The fractional derivative is considered in the Caputo sense. This technique is based on generalized Operational matrix of triangular functions. The introduced method reduces the proposed problem for solving a system of algebraic equations. Illustrative examples are included to demonstrate the validity and the applicability of the proposed method...

In this article we implement an Operational matrix of fractional integration for Legendre polynomials. We proposed an algorithm to obtain an approximation solution for fractional differential equations, described in Riemann-Liouville sense, based on shifted Legendre polynomials. This method was applied to solve linear multiorder fractional differential equation with initial conditions, and the exact solutions obtained for some illustrated examples. Numerical results reveal that this method gives ideal approximation for linear multi-order fractional differential equations.