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.

Magnetic nanoparticles (MNPs) of iron oxide (Fe₃O₄) represent the most promising materials in many applications. MNPs have been synthesized by co-precipitation of ferric and ferrous ions in alkaline solution. Two methods of synthesis were conducted with different parameters, such as temperature (25 and 80 ̊C), adding a base to the reactants and the opposite process, and using nitrogen as an inert gas. The product of the first method (MNPs-1) and the second method (MNPs-2) were characterized by x-ray diffractometer (XRD), Zeta Potential, atomic force microscope (AFM) and scanning electron microscope (SEM). AFM results showed convergent particle size of (MNPs-1) and (MNPs-2) with (86.01) and (74.14)

A field experiment was carried out during winter season of 2019 at Al-Muradiya research state, Babylon government, Iraq, to study the role of the sprayed types of potassium fertilizer in improving of flag leaf contribution in grain yield of wheat. The layout of the experiment was randomized complete block design in factorial arrangement at three replicates. The experiment included spraying common and nano potassium fertilizer at booting stage, in addition to control treatment (spraying of distilled water) as a first factor, and removal treatments (removal of flag leaf at 10% anthesis stage and nonremoval) as a second factor. The results showed that the spraying of nano potassium fertilizer was significantly superior in the dry matter transp

Nitrogen (N) and phosphorus (P) are the most important nutrients for crop production. The N contributes to the structural component, generic, and metabolic compounds in a plant cell. N is mainly an essential part of chlorophyll, the compound in the plants that is responsible for photosynthesis process. The plant can get its available nitrogen from the soil by mineralizing organic materials, fixed-N by bacteria, and nitrogen can be released from plant as residue decay. Soil minerals do not release an enough amount of nitrogen to support plant; therefore, fertilizing is necessary for high production. Phosphorous contributes in the complex of the nucleic acid structure of plants. The nucleic acid is essential in protein synthesis regulation; t

Results showed that the optimum conditions for production of inulunase from isolate Kluyveromyces marxianus AY2 by submerged culture could be achieved by using inulin as carbon source at a concentration of 2% with mixture of yeast extract and ammonium sulphate in a ratio of 1:1 in a concentration of 1% at initial pH 5.5 after incubation for 42 hours at 30ºC.

Two field experiments were conducted during the season 2021-2022 in central Iraq represented by the Al-Muthanna governorate - Al-Majd District and Al-Qadisiyah governorate / Al-Nouriah Research Station to determine the productivity of the Baghdad 3 cultivar from spray foliar fertilization of Macro and Micro elements with alcoholic sugars and half the fertilizer recommendation for addition floor, three treatments were used for fertilization: T1 as the control treatment and T2 with alcoholic sugar fertilization at a concentration of 20 g.L-1 + the fertilizer combination of Macro and Micro elements, and T3 with alcoholic sugar fertilization at a concentration of 40 g.L-1 + the fertilizer combination of Macro and Microelements, at irrigation 55

The purpose of this paper is to examine absorbance for the removal of the Red Congo using wheat husk as a biological pesticide. Several experiments have been conducted with the aim of configuring breakthrough data in a fluidized bed reactor. The minimum fluidized velocities of the bed were found to be 0.031 mm/s for mish sizes of (250) µm diameter with study the mass transfer be calculated K_L values. The results showed a well-fitting with the experimental data. Different operating conditions were selected: bed height (2, 5 and 10) cm, flow rate (90, 100and 120) ml/sec and particle diameter (250, 600, 1000) µm. The breakthrough curves were plotted for Congo Red, Values showed that the lower the bed, the lower the number of ad