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.

Abstract In this study, an investigation is conducted to realise the possibility of organic materials use in radio frequency (RF) electronics for RF-energy harvesting. Iraqi palm tree remnants mixed with nickel oxide nanoparticles hosted in polyethylene, INP substrates, is proposed for this study. Moreover, a metamaterial (MTM) antenna is printed on the created INP substrate of 0.8 mm thickness using silver nanoparticles conductive ink. The fabricated antenna performances are instigated numerically than validated experimentally in terms of S11 spectra and radiation patterns. It is found that the proposed antenna shows an ultra-wide band matching bandwidth to cover the frequencies from 2.4 to 10 GHz with bore-sight gain variation from 2.2 to

The effect of high energy radiation on the energy gap of compound semiconductor Silicon Carbide (SiC) are viewed. Emphasis is placed on those effects which can be interpreted in terms of energy levels. The goal is to develop semiconductors operating at high temperature with low energy gaps by induced permanent damage in SiC irradiated by gamma source. TEACO2 laser used for producing SiC thin films. Spectrophotometer lambda - UV, Visible instrument is used to determine energy gap (Eg). Co-60, Cs-137, and Sr-90 are used to irradiate SiC samples for different time of irradiation. Possible interpretation of the changing in Eg values as the time of irradiation change is discussed

This paper deals with the Magnetohydrodynyamic (Mill)) flow for a viscoclastic fluid of the generalized Oldroyd-B model. The fractional calculus approach is used to establish the constitutive relationship of the non-Newtonian fluid model. Exact analytic solutions for the velocity and shear stress fields in terms of the Fox H-function are obtained by using discrete Laplace transform. The effect of different parameter that controlled the motion and shear stress equations are studied through plotting using the MATHEMATICA-8 software.

The study aimed to determine of some Optimum conditions for bioremediation and removing of seven mineral elements included hexavalent chromium, nickel, cobalt, cadmium, lead, iron and copper as either alone or in group by living and heat treated cells of baker’s yeast Saccharomyces cerevisiae. The dried baker's yeast from Aldnaamaya China Company was used in this study. Biochemical tests was used to ensure yeast belonging to S. cerevisiae and then used to remove the mentioned mineral elementes under different conditions which included incubation period, pH, and temperature. It was found that the best of these conditions was 60 minutes for duration of incubation, 6 for pH, 25 ᵒC for temperature. During the study the behavior of living

Design of experiments (DOE) was made by Minitab software for the study of three factors used in the precipitation process of the Sodium Aluminate solution prepared from digestion of α-Al₂O₃  to determine the optimum conditions to a produce Boehmite which is used in production of ɤ-Al₂O₃ during drying and calcination processes, the factors are; the temperature of the sodium aluminate solution, concentration of HCl acid added for the precipitation and the pH of the solution at which the precipitation was ended. The design of the experiments leads to 18 experiments.

   The results show that the optimum conditions for the precipitation of the sodium aluminate solution which

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

We describe the synthesis and characterization of a novel 2D-MnOx material using a combination of HR-TEM, XAS, XRD, and reactivity measurements. The ease with which the 2D material can be made and the conditions under which it can be made implies that water oxidation catalysts previously described as “birnessite-like” (3D) may be better thought of as 2D materials with very limited layer stacking. The distinction between the materials as being “birnessite-like” and “2D” is important because it impacts on our understanding of the function of these materials in the environment and as catalysts. The 2D-MnOx material is noted to be a substantially stronger chemical oxidant than previously noted for other birnessite-like manganese oxi