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.

Nimodipine (NMD) is a dihydropyridine calcium channel blocker useful for the prevention and treatment of delayed ischemic effects. It belongs to class ? drugs, which is characterized by low solubility and high permeability. This research aimed to prepare Nimodipine nanoparticles (NMD NPs) for the enhancement of solubility and dissolution rate. The formulation of nanoparticles was done by the solvent anti-solvent technique using either magnetic stirrer or bath sonicator for maintaining the motion of the antisolvent phase. Five different stabilizers were used to prepare NMD NPs( TPGS, Soluplus®, HPMC E5, PVP K90, and poloxamer 407). The selected formula F2, in which  Soluplus 

has been utilized as a stabilizer, has a par

It is widely accepted that early diagnosis of Alzheimer's disease (AD) makes it possible for patients to gain access to appropriate health care services and would facilitate the development of new therapies. AD starts many years before its clinical manifestations and a biomarker that provides a measure of changes in the brain in this period would be useful for early diagnosis of AD. Given the rapid increase in the number of older people suffering from AD, there is a need for an accurate, low-cost and easy to use biomarkers that could be used to detect AD in its early stages. Potentially, the electroencephalogram (EEG) can play a vital role in this but at present, no reliable EEG biomarker exists for early diagnosis of AD. The gradual s

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

Solar cells thin films were prepared using polyvinyl alcohol (PVA) as a thin film, with extract of natural pigment from local flower. A concentration of 0.1g/ml of polyvinyl alcohol solution in water was prepared for four samples, with various concentrations of plant pigment (0, 15, 25 and 50) % added to each of the four solutions separately for preparing (PVA with low concentrated dye , PVA with medium concentrated dye and PVA with high concentrated dye ) thin films respectively . Ultraviolet absorption regions were obtained by computerized UV-Visible (CECIL 2700). Optical properties including (absorbance, reflectance, absorption coefficient, energy gap and dielectric constant) via UV- Vis were tested, too.  Fourier transform infra

The loose sand is subject to large settlement when it is exposed to high stresses. This settlement is due to the nature of the high drainage of sand, which displays foundations and constructions to a large danger. The densification of loose sandy soils is required to provide sufficient bearing capacity for the structures. Thus soil stabilization is used to avoid failure in the facilities. Traditional methods of stabilized sandy soil such as fly ash, bituminous, and cement often require an extended curing period. The use of polymers to stabilize sandy soils is more extensive nowadays because it does not require a long curing time in addition to being chemically stable. In this study, the effect of adding different percent