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 problem of the study and its significance:
Due to the increasing pressures of life continually, and constant quest behind materialism necessary and frustrations that confront us daily in general, the greater the emergence of a number of cases of disease organic roots psychological causing them because of severity of a lack of response to conventional treatments (drugs), and this is creating in patients a number of emotional disorders resulting from concern the risk of disease
That is interested psychologists and doctors searchin
... Show MoreThe rate of gas induction was measured in gas-inducing type mechanically agitated contactors provided with two impellers. A reactor of 0.5 m i.d. was used with a working capacity of 60 liters of liquid. Tap water was used as the liquid phase, and air was used as the gas phase. The bioreactor mixing system consists of two equal diameter stirrers; the top impeller is shrouded-disk/curved-blade turbine with six evacuated bending blades, while the bottom impeller was disk turbine. The impeller speed was varied in the range of 50 to 800 rpm. The ratio of impeller diameter to tank diameter (D/T) and the submergence (S) of upper impeller from the top were varied. The effects of clearance of lower impeller from the tank bottom (C2) an
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In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit
... Show MoreA novel analytical method is developed for the determination of azithromycin. The method utilizes continuous flow injection analysis to enhance the chemiluminescence system of luminol, H2O2, and Cr(III). The method demonstrated a linear dynamic range of 0.001–100 mmol L-1 with a high correlation coefficient (r) of 0.9978, and 0.001–150 mmol L-1 with a correlation coefficient (r) of 0.9769 for the chemiluminescence emission versus azithromycin concentration. The limit of detection (L.O.D.) of the method was found to be 18.725 ng.50 µL−1 based on the stepwise dilution method for the lowest concentration within the linear dynamic range of the calibration graph. The relative standard deviation (R.S.D. %) for n = 6 was less than 1.2%
... Show MoreThe evolution of thought, planning for Urban Communities in the second half of the twentieth century, through several successive stages. He was thought of planning urban communities depends on identifying the general plan for land uses of the project area as a basis for drawing charts the physical, social, economic, and put the general plan for land uses based on the terms of reference set by the number of experts in the ministries and agencies. I have lived cities in the Arab-Muslim region, during the transition period the natural and historic environment, urban, sophisticated balanced ways mentioned in the cultural, social, inspired by the teachings of Islam and the customs and traditions of the Arab social, put forth a set of
... Show MoreThis work aims to find a solution to the problem under investigation and to study non-local boundary-value problems for rectangular domains and two-dimensional thirdorder partial differential equations (PDEs). A finite-difference method combined with the trapezoidal rule is used to solve problems. The numerical results were determined to be steady and accurate.
Teen-Computer Interaction (TeenCI) stands in an infant phase and emerging in positive path. Compared to Human-Computer Interaction (generally dedicated to adult) and Child-Computer Interaction, TeenCI gets less interest in terms of research efforts and publications. This has revealed extensive prospects for researchers to explore and contribute in the region of computer design and evaluation for teen, in specific. As a subclass of HCI and a complementary for CCI, TeenCI that tolerates teen group, should be taken significant concern in the sense of its context, nature, development, characteristics and architecture. This paper tends to discover teen’s emotion contribution as the first attempt towards building a conceptual model for TeenC
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