In this article, we investigate a mathematical fractional model of tuberculosis that takes into account vaccination as a possible way to treat the disease. We use an in-host tuberculosis fractional model that shows how Macrophages and Mycobacterium tuberculosis interact to knowledge of how vaccination treatments affect macrophages that have not been infected. The existence of optimal control is proven. The Hamiltonian function and the maximum principle of the Pontryagin are used to describe the optimal control. In addition, we use the theory of optimal control to develop an algorithm that leads to choosing the best vaccination plan. The best numerical solutions have been discovered using the forward and backward fractional Euler

The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.

This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.

In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.

This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.

An adaptive nonlinear neural controller to reduce the nonlinear flutter in 2-D wing is proposed in the paper. The nonlinearities in the system come from the quasi steady aerodynamic model and torsional spring in pitch direction. Time domain simulations are used to examine the dynamic aero elastic instabilities of the system (e.g. the onset of flutter and limit cycle oscillation, LCO). The structure of the controller consists of two models :the modified Elman neural network (MENN) and the feed forward multi-layer Perceptron (MLP). The MENN model is trained with off-line and on-line stages to guarantee that the outputs of the model accurately represent the plunge and pitch motion of the wing and this neural model acts as the identifier. Th