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 designer must find the optimum match between the object's technical and economic needs and the performance and production requirements of the various material options when choosing material for an engineering application. This study proposes an integrated (hybrid) strategy for selecting the optimal material for an engineering design depending on design requirements. The primary objective is to determine the best candidate material for the drone wings based on Ashby's performance indices and then rank the result using a grey relational technique with the entropy weight method. Aluminum alloys, titanium alloys, composites, and wood have been suggested as suitable materials for manufacturing drone wings. The requirement

Pure and Fe-doped zinc oxide nanocrystalline films were prepared
via a sol–gel method using -
C for 2 h.
The thin films were prepared and characterized by X-ray diffraction
(XRD), atomic force microscopy (AFM), field emission scanning
electron microscopy (FE-SEM) and UV- visible spectroscopy. The
XRD results showed that ZnO has hexagonal wurtzite structure and
the Fe ions were well incorporated into the ZnO structure. As the Fe
level increased from 2 wt% to 8 wt%, the crystallite size reduced in
comparison with the pure ZnO. The transmittance spectra were then
recorded at wavelengths ranging from 300 nm to 1000 nm. The
optical band gap energy of spin-coated films also decreased as Fe
doping concentra

In this work, (CdO)1-x (CoO)x thin films were prepared on glass slides by laser-induced plasma using Nd:YAG laser with (λ=1064 nm) and duration (9 ns) at different laser energies (200-500 mJ) with ratio (x=0.5), The influence of laser energy on structural and optical properties has been studied. XRD patterns show the films have a structure of polycrystalline wurtzite. As for AFM tests results for the topography of the surface of the film, where the results showed that the grain size and the average roughness increase with increasing laser energy. The optical properties of all films were also studied and the results showed that the absorption coefficient for within the wavelength range (280-1100 nm), The value of the optical power gap fo

Thin films of (CdO)x (CuO)1-x (where x = 0.0, 0.2, 0.3, 0.4 and 0.5) were prepared by the pulsed laser deposition. The CuO addition caused an increase in diffraction peaks intensity at (111) and a decrease in diffraction peaks intensity at (200). As CuO content increases, the band gap increases to a maximum of 3.51 eV, maximum resistivity of 8.251x 104 Ω.cm with mobility of 199.5 cm2 / V.s, when x= 0.5. The results show that the conductivity is ntype when x value was changed in the range (0 to 0.4) but further addition of CuO converted the samples to p-type.

Aqueous root extract has been used to examine the green production of silver nanoparticles (AgNPs) by reducing the Ag+ ions in a silver nitrate solution. UV-Vis spectroscopy, X-ray diffraction, field emission scanning electron microscopy, and Fourier transform infrared spectroscopy (FTIR) were used to analyze the produced AgNPs. The AgNPs that were created had a maximum absorbance at 416 nm, were spherical in form, polydispersed in nature, and were 685 nm in size.The AgNPs demonstrated antibacterial efficacy against Escherichia coli and Staphylococcus. The dengue vector Aedes aegypti's second instar larvae were very susceptible to the AgNPs' powerful larvicidal action.

Nonlinear diffraction patterns can be obtained by focusing a laser beam through a thin slice of the material. Here, we investigated experimentally the formation of the far field nonlinear diffraction patterns of cw laser beam at 532 nm passing through a quartz cuvette containing multi-wall carbon nanotubes (MWCNT's) suspended in acetone and in DI water at concentrations of 0.030.wt.%, 0.045 wt.%, 0.060 wt.%, and 0.075 wt.%. Our results show that increasing the concentration of both types of suspensions (MWCNTs in acetone and MWCNTs DI water) led to increase in the number of pattern rings which indicates an increase in their nonlinear refractive indices. Moreover, MWCNTs DI water suspension at a concentration of 0.075 wt. % was more effic