Journal of Applied & Computational Mathematics

We propose in this article one method of numerical resolution using the programming under Matlab of one of the fractional differential equations of Euler-Lagrange containing a composition of the left and right fractional derivatives of order α, 0< α<1, of Riemann-Liouville and Caputo respectively.

We introduced an algorithm to solve a Non Linear Constrained Optimization (NLCO) problem in this paper. This algorithm follows Das’s idea of Newton’s interiorpoint method that uses a diagonal matrix of Coleman and Li for NLCO problems. A Trust-Region (T-R) mechanism is used to globalize the algorithm. This algorithm follows Byrd and Omojokun’s idea of step decomposition. It is a successful idea to overcome the difficulty of having an infeasible quadratic T-R sub problem and converts the quadratic T-R sub problem into two unconstrained T-R sub problems.

A global convergence theory of the algorithm is studied under five standard assumptions. This algorithm is different and maybe simpler than similar ideas such that the global convergence theory is not depending on the linear independence assumption on the gradients of the constraints.

Some numerical tests are stated to indicate that the algorithm performs effectively and efficiently in pursuance.

Imagine a world that allows for open, unmonitored communication, and the ability to trade currency between individuals anonymously. An environment such as this would present itself as a prime location for malicious intent. Money laundering, exploitation, theft, harassment, and stalking could potentially go unnoticed. When discussing World of warcraft or fortnite, malicious intent would generally not come to mind. However, this is precisely the type of environment that massively multiplayer online role-playing games provide.

In this work, we used the 0de45 to simulate the behavior of the dynamical system of the nonlinear system of ordinary differential equation at equilibrium. It is shown that if the forest resources is maintained at the given equilibrium, the activities of man will not affect the stability of the forest resource biomass but a little below the equilibrium the system will be unstable.

The present paper is intended to study of the evolution of Electric and Magnetic parts of Weyl tensor in a space-time; in particular to measure the components of parts of Weyl tensor of an observer with a time-like 4-unit vector we have attempted to describe the tensors, which are the parts of Weyl tensor concerning for to the observeru. Further, we have established that if eigenvalues of any matrix are zero, real and imaginary then it is a part of Weyl tensor. Afterward, the cases from Petrov types have been obtained therein.