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.

In this paper, we deal with a dynamical system that can demonstrate a chaotic attractor of Rossleroscillator. We simulate the Rosslerequations numerically then we investigate the model experimentally. Numerically, the Rossler parameter a and b were fixed and c was changed.The evolution of the system exhibits period, period-doubling, second period doubling, and chaos when control parameters are changed. This evolution can be seen by analyze the time series, the bifurcation diagrams and phase space. Experimentally, the evolution of the system exhibited the same numerical behavior by changing the resistance (Rv) in Rossler circuit that represent as control parameter.

The reticuloendothelial system (RES) play an important role in immunity against bacterial infection and Klebsiella pneumoniae one of the most common causes of hospital-acquired infections. Dextran70 (D70), a polysaccharide, may alter functions of this system through changing many biological activities in the tissues.

Laser is a powerful device that has a wide range of applications in fields ranging from materials science and manufacturing to medicine and fibre optic communications. One remarkable

The A2?u-X1?g+ emission band system of 7LiH1 molecule has been calculated for Lambda doubling. The relation between wave number ?p , ?Q , ?R conducted the energies of the state of rotation F (J), and (J + 1) with rotational quantum number J, respectively, of 7LiH1 molecule for statehood A2?u using the rotation, fixed vibrational states of both the ground and raised crossovers vibrational against ???= 0 to V ' = 0-4using rotational levels J = 0 to J = 20 have found.

A 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%

A mathematical eco-epidemiological model consisting of harvested prey–predator system involving fear and disease in the prey population is formulated and studied. The prey population is supposed to be separated into two groups: susceptible and infected. The susceptible prey grows logistically, whereas the infected prey cannot reproduce and instead competes for the environment’s carrying capacity. Furthermore, the disease is transferred through contact from infected to susceptible individuals, and there is no inherited transmission. The existence, positivity, and boundedness of the model’s solution are discussed. The local stability analysis is carried out. The persistence requirements are established. The global behavior of th

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