The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

Water pollution as a result of contamination with dye-contaminating effluents is a severe issue for water reservoirs, which instigated the study of biodegradation of Reactive Red 195 and Reactive Blue dyes by E. coli and Bacillus sp. The effects of occupation time, solution pH, initial dyes concentrations, biomass loading, and temperature were investigated via batch-system experiments by using the Design of Experiment (DOE) for 2 levels and 5 factors response surface methodology (RSM). The operational conditions used for these factors were optimized using quadratic techniques by reducing the number of experiments. The results revealed that the two types of bacteria had a powerful effect on biodegradable dyes. The regression analysis reveale

Peer-Reviewed Journal

The study of biopolymers and their derivative materials had received a considerable degree of attention from researchers in the preparation of novel material. Biopolymers and their derivatives have a wide range of applications as a result of their bio-compatibility, bio-degradability and non-toxicity. In this paper, chitosan reacted with different aldehydes(2,4 –dichloro- benzaldehyde or 2-methyl benzaldehyde), different ketones (4-bromoacetophenone or 3-aminoacetophenone) to produce chitosan schiff base (1-4) . Chitosan schiff base (1-4) reacted with glutaric acid or adipic acid in acidic media in distilled water according to the steps of Fischer and Speier to produce compounds (5-12)

In this work we used the environmentally friendly method to prepared ZrO2 nanoparticles utilizing the extract of Thyms plant In basic medium and at pH 12, the ZrO2 NPs was characterized by different techniques such as FTIR, ultraviolet visible, Atomic force microscope, Scanning Electron Microscopy, X-ray diffraction and Energy dispersive X-ray. The average crystalline size was calculated using the Debye Scherres equation in value 7.65 nm. Atomic force microscope results showed the size values for ZrO2 NPs were 45.11nm, and there are several distortions due to the presence of some large sizes. Atomic force microscope results showed the typical size values for ZrO2 NPs were 45.11 nm, and there are several distortions due to the presence of so

The consumption of fossil fuels has caused many challenges, including environmental and climate damage, global warming, and rising energy costs, which has prompted seeking to substitute other alternative sources. The current study explored the microwave pyrolysis of Albizia branches to assess its potential to produce all forms of fuel (solid, liquid, gas), time savings, and effective thermal heat transfer. The impact of the critical parameters on the quantity and quality of the biofuel generation, including time, power levels, biomass weight, and particle size, were investigated. The results revealed that the best bio-oil production was 76% at a power level of 450 W and 20 g of biomass. Additionally, low power levels led to enhanced