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.

Background: Radiation therapy has the ability to destroy healthy cells in addition to cancer cells in the area being treated. However, when radiation combines with doxorubicin, it becomes more effective on breast cancer treatment. Objective: This study aims to clarify the effect of X-ray from LINAC combined with amygdalin and doxorubicin on breast cancer treatment, and the possibility of using amygdalin with X-ray instead of doxorubicin for the breast cancer treatment. Method: Two cell lines were used in this study, the first one was MCF-7 cell line and second one was WRL- 68 normal cell line. These cells were preserved in liquid nitrogen, prepared, developed and tested in the (place). The effect of three x-ray doses combined with a

Background: Sclerotherapy is a simple treatment modality for treatment of infantile hemangioma and slow-flow vascular malformations; Polidocanol is a mild sclerosing agent that is traditionally used in treatment of varicose veins. This study aims to evaluate the effectiveness, treatment outcome, and complications of polidocanol foam sclerotherapy for infantile hemangioma and slow-flow vascular malformations. Materials and methods: Between March 2013 and December 2014, seventeen patients with infantile hemangioma and slow-flow vascular malformations treated with polidocanol 1% foam sclerotherapy. Foam was prepared by Tessari’s method. Injection performed under general or local anesthesia, injections were repeated (if necessary) on mon

Iron slag is a byproduct generated in huge quantities from recycled remnants of iron and steel factories; therefore, the possibility of using this waste in the removal of benzaldehyde from contaminated water offers an excellent topic in sustainability field. Results reveal that the removal efficiency was equal to 85% for the interaction of slag and water contaminated with benzaldehyde at the best operational conditions of 0.3 g/100 mL, 6, 180 min, and 250 rpm for the sorbent dosage, initial pH, agitation time, and speed, respectively with 300 mg/L initial concentration. The maximum uptake capacity of iron slag was 118.25 mg/g which was calculated by the Langmuir model. Physical sorption may be the major mechanism for the removal of

The current investigation examines the combined impacts of ultrasonic radiation and hydrogen donors on the viscosity of heavy crude oil. The impact of exposure time, power, duty cycle, and temperature on the viscosity of Iraqi heavy crude oil with 20.32 API was studied. Also, the viscosity of the oil samples, which were mixed with a hydrogen donor (decalin) and subjected to ultrasonic treatment under optimal conditions, was examined to evaluate the combined impact of ultrasonic radiation and hydrogen donor on the viscosity of crude oil. The viscosity experienced a decrease of 52.34% at 2 min of irradiation, 360 W ultrasonic power, 0.8 duty cycle, 35 ⁰C, and 8vol% decalin. To validate the outcomes of the experiments, asphaltene content, s

Radiation treatment has long been the conventional approach for treating nasopharyngeal cancer (NPC) tumors due to its anatomic features, biological characteristics, and radiosensitivity. The most common treatment for nasopharyngeal carcinoma is radiotherapy. This study aimed to assess the better quality of radiotherapy treatment techniques using intensity-modulated radiotherapy (IMRT) and volumetric-modulated arc therapy (VMAT). The VMAT and IMRT are comparative techniques. Forty patients with nasopharyngeal carcinoma and forwarded for radiotherapy were treated with both advanced techniques, IMRT and VMAT, using eclipse software from Varian. The x-ray energy was set at 6 MV. The total prescribed dose was 70 Gy. The results show that the

Background: Recurrent aphthous ulceration (RAU) is an inflammatory condition of unknown etiology characterized by painful recurrent (single or multiple) ulcerations of the oral mucosa. It is one of the most common and poorly understood mucosal disorders. It occurs more frequently in times of stress. Local and systemic conditions, genetic, immunologic, microbial factors, and oxidative stress may play a role in the pathogenesis of RAU. The objective of this study was to evaluate the free radical metabolism and antioxidant activity of RAU patients treated by lavender or flax oil paint.

Materials and Methods: Sixty-six RAU patients were enroll