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 present paper investigates the role of fear and predator dependent refuge in the prey-predator system. The system describes the interaction between prey and a stage structure of predator that incorporates Holling II functional response. The predator splits into two compartments immature (juvenile) and mature (adult). The mature predators can hunt and reproduce but this capability is not found in the immature predators, the immature depend on their parents. The growth rate of prey decreases due to the existence of mature predators. The existence, uniqueness, and boundedness of the solution of the system are investigated. Three equilibrium points of the system are determined. The local stability of the system is studied. The global stabil

Vanadium dioxide nanofilms are one of the most essential materials in electronic applications like smart windows. Therefore, studying and understanding the optical properties of such films is crucial to modify the parameters that control these properties. To this end, this work focuses on investigating the opacity as a function of the energy directed at the nanofilms with different thicknesses(1–100) nm. Effective mediator theories(EMTs), which are considered as the application of Bruggeman’s formalism and the Looyenga mixing rule, have been used to estimate the dielectric constant of VO2 nanofilms. The results show different opacity behaviors at different wavelength ranges(ultraviolet, visible, and infrared). The results depict that th

Non thermal argon plasma needle at atmospheric pressure was constructed. The experimental set up was based on simple and low cost electric components that generate electrical field sufficiently high at the electrodes to ionize various gases which flow at atmospheric pressure. A high AC power supply was used with 9.6kV peak to peak and 33kHz frequency. The plasma was generated using two electrodes. The voltage and current discharge waveform were measured. The temperature of Ar gas plasma jet at different gas flow rate and distances from the plasma electrode was also recorded. It was found that the temperature increased with increasing frequency to reach the maximum value at 15 kHz, and that the current leading the voltage, which demonstra

The alloys of CdSe1-xTex compound have been prepared from their elements successfully with high purity (99.9999%) which mixed stoichiometry ratio (x=0.0, 0.25, 0.5, 0.75 and 1.0) of (Cd, Se and Te) elements. Films of CdSe1-xTex alloys for different values of composition with thickness(0.5?m) have been prepared by thermal evaporation method at cleaned glass substrates which heated at (473K) under very low pressure (4×10-5mbar) at rate of deposition (3A?/s), after that thin films have been heat treated under low pressure (10-2mbar) at (523K) for two hours. The optical studies revealed that the absorption coefficient (?) is fairly high. It is found that the electronic transitions in the fundamental absorption edge tend to be allowed direct tr

Studied the optical properties of the membranes CdS thin containing different ratios of ions cadmium to sulfur attended models manner spraying chemical gases on the rules of the glass temperature preparation (350c) were calculated energy gap allowed direct these membranes as observed decrease in the value of the energy gap at reducing the proportion ofsulfur ions as absorption coefficient was calculated

Thin films of tin sulfide (SnS) were prepared by thermal evaporation technique on glass substrates, with thickness in the range of 100, 200 and 300nm and their physical properties were studied with appropriate techniques. The phase of the synthesized thin films was confirmed by X-ray diffraction analysis. Further, the crystallite size was calculated by Scherer formula and found to increase from 58 to 79 nm with increase of thickness. The obtained results were discussed in view of testing the suitability of SnS film as an absorber for the fabrication of low-cost and non toxic solar cell. For thickness, t=300nm, the films showed orthorhombic OR phase with a strong (111) preferred orientation. The films deposited with thickness < 200nm deviate