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.

There is confusion between the concept of honesty and credibility arguing that their meaning is the same. ‘Credibility; is derived from the truth which means evidence of honesty, while ‘honesty’ means not lying and matching reality. The study of credibility begins globally at the end of the fifties of the second millennium to see the decline and refrain from reading newspapers, while it was studied in the Arab world in 1987. Global studies find several meanings of the concept of ‘credibility’ such as accuracy, completeness, transfer facts, impartiality, balance, justice, objectivity, trust, honesty, respect the freedom of individuals and community, and taking into account the traditions and norms.
Credibility has two dimens

     Some geometric parameters affecting the performance of a wire-plate electrostatic precipitator (ESP) are investigated theoretically. A numerical model was built to investigate the influence of the discharge wire size, wire separation, collector plates spacing, and roughness factor on the ESP performance. The results show that thinner wires emit higher current than larger ones at the same applied voltage, which would be suitable for low voltage power supply to generate the desired current density at the collecting electrodes. The results also show that, as the discharge electrodes get closer, the corona gets suppressed, resulting in a diminished corona current flow. On the other hand, as the distance between elect

You Mohammed, you're prophet of God and I'm Gabriel)). With this heavenly call which Mohammed, the messenger of God (may God's mercies be on him), got and when he left Hiraa cave and after getting the aye ((read with your God's name)), a new period of mankind's history started. From that time, the greatest state was established. There was no public treasury and no public financial resources at that time. Abu Baker (God bless him) spent a lot of money to support the costs of the new mission. After Al-Hijra, the bases of establishing the Islamic state were available but it lacked administrative and financial organizing. Therefore the prophet was very keen to find Islamic system which ensures justice and availability of

The aim of the study was to evaluate the efficacy of diode laser (λ=940 nm) in the management of gingival hyperpigmentation compared to the conventional bur method. Materials and methods: Eighteen patients with gingival hyperpigmentation were selected for the study with an age between 12-37 years old. The site of treatment was the upper gingiva using diode laser for the right half and the conventional method for the left half. All patients were re-evaluated after the following intervals: 3 days, 7 days, 1 month and 6 months post-operation. Pain and functions were re-evaluated in each visit for a period of 1 day, 3 days and 1 week post-operation. Laser parameters included 1.5 W in continuous mode with an initiated tip (400 μm) placed in

The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

Positive and negative parity states for 114Te have been studied applying the vibration al limit U(5) of Interacting boson model (IBM- 1 ) . The present results have shown their good agreement with experimental data in addition to the determination of the spin/parity of new energy levels are not assigned experimentally as the levels 0+2 and 5+1 and the levels 3"1 and 5-1 . Then back propagation multiLayer neural network used for positive and negative parity states for 114Te and shown their membership to the Vibration limit U(5) the network implemented by MATLAB system.

This study included the effect of chronic exposure of different concentrations of sodium chloride on the freshwater Crustacean Daphinea pulex from the order of Cladocera. The concentrations used for the chronic exposure were( 0.1‰, 0.5‰, 1‰, 1.5‰, 2‰ )to investigate the effect on the some reproductive parameter which included mean number of eggs and juveniles produced per female and per clutch,and mean number of clutch per female which decline from (6.0) clutch/female in the control treatment to (3.0) clutch/female in (2‰) concentrations, as well as to investigate the number of females produce the clutches and we found only one female produced six cluthes in the( 2‰) concentration of sodium chlor

Flow-production systems whose pieces are connected in a row may not have maintenance scheduling procedures fixed because problems occur at different times (electricity plants, cement plants, water desalination plants). Contemporary software and artificial intelligence (AI) technologies are used to fulfill the research objectives by developing a predictive maintenance program. The data of the fifth thermal unit of the power station for the electricity of Al Dora/Baghdad are used in this study. Three stages of research were conducted. First, missing data without temporal sequences were processed. The data were filled using time series hour after hour and the times were filled as system working hours, making the volume of the data relativel