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.

The use of medicinal plant preparations to clean and disinfect root canal infection is gaining popularity. The aim of this study was to evaluate the bioactive composition of leaf extracts of Moringa oleifera plants cultivated in Iraq (specifically Baghdad) and their antimicrobial activity against selected root canal pathogens for potential application in endodontic treatment. Materials and Methods. Moringa leaf extracts were prepared either through cold maceration or warm digestion techniques to perform an ethanolic or aqueous extraction, respectively. Phytochemical detection was performed before thin layer chromatography (TLC) and high-performance liquid chromatography (HPLC) to measure flavonoids and phenolic compounds within both

Mesoporous silica (MPS) nanoparticle was prepared as carriers for drug delivery systems by sol–gel method from sodium silicate as inexpensive precursor of silica and Cocamidopropyl betaine (CABP) as template. The silica particles were characterized by SEM, TEM, AFM, XRD, and N2adsorption–desorption isotherms. The results show that the MPS particle in the nanorange (40-80 nm ) with average diameter equal to 62.15 nm has  rods particle morphology, specific surface area is 1096.122 m²/g, pore volume 0.900 cm³/g, with average pore diameter 2.902 nm, which can serve as efficient carriers for drugs. The adsorption kinetic of Ciprofloxacin (CIP) drug was studied and the data were analyzed and found to match well with

This study designed to prepare ultrafine apixaban (APX) o/w nanoemulsion (NE) based gel with droplet size below 50 nm as a good method for transdermal APX delivery without using permeation enhancer, alternatively, the formulation components itself act as permeation enhancer. APX, a potent oral anticoagulant drug that selectively and directly inhibit coagulation factor Xa, was selected as a good candidate for transdermal delivery as it displays poor water solubility (0.028 mg/mL) and low bioavailability (50%). APX-NE gel was prepared using triacetin, triton-x-100 and carbitol as oil phase, surfactant and cosurfactant respectively, while Carbopol 940 used as a gelling agent. Ex vivo permeation of APX-NE gel through human stratum c