This article introduces a novel procedure to detect an approximate solution to Fredholm fractional integro-differential equations with linear type (LFFIDE) defined using Caputo fractional derivative. The new procedure approximates the solution using three types of polynomials: Laguerre polynomials, Hermite polynomials, and Legendre polynomials, thereafter transforming the problem into a linear programming problem. The approximate solutions are compared using testing examples to examine the efficiency of the suggested approach. Also, a comparison with the other methods using the same polynomials illustrates The effectiveness and consistency of the proposed technique. Finally, the error analysis of the proposed technique and convergent are di

This study investigated the bioethanol production from green algae Chlorella vulgaris depending on its carbohydrate-enriched biomass. Four different phosphorous concentrations were employed to stimulate bioethanol production from Chlorella vulgaris. The impact of various phosphorous values on Chlorella vulgaris growth rate as well as primary product (carbohydrate) were evaluated. High performance liquid chromatography was utilized in this work. The stationary phase was identified as day 14, 12, 10 and 6 in treatments 6, 4, 2 and g/L, respectively. The findings suggest that the treatment without phosphorous addition had the highest record of carbohydrate content (22.64% dry weight) as well as the highest bioethanol yield (20.66% dry weight).

In this work, the dyes Rhodamine B and Coumarin 102 containing titanium dioxide nanoparticles were used as scattering centers to fabricate a random gain medium. The laser dye was dissolved in hexanol and methanol solvent respectively. The titanium dioxide nanoparticles were synthesized by DC reaction magnetron spraying technique. The random-gain medium was made by adding 2.5 mg of titanium dioxide nanoparticles to Rhodamine and coumarin 102 dyes by coating the glass cell with two-sided titanium dioxide with high spectral efficiency and low production cost. A narrow line optical emission was detected at 565 nm for Rhodamine B and 534 nm for coumarin 102, where it was found that rhodamine B dye has FWHM 8 nm and coumarin dye 102 has FWHM 9 nm