In this paper, numerical methods for solving fractional differential equations by using a triangle neural network are proposed. The derivative is considered Caputo type. of the analyzed first. Then, based on technique minimizing loss function network, proposed reduce equation into gradient descent problem or quadratic optimization problem. By process process, solution to FDEs can be obtained. e...

To show the potential of non-commensurable fractional-order dynamical systems in modeling epidemiological phenomena, we will adjust parameters a fractional generalization SIR model to describe population distributions generated by SARS-CoV-2 France and Colombia. Despite completely different contexts both countries, see how system presented here manages adequately them thanks flexibility provide...

In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose exact confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the fractional Brownian motion is known or unknown are investigated. These intervals are obtained by observing a single discretized sample path of a fractional ...

The Quadratic Convex Reformulation (QCR) method is used to solve quadratic unconstrained binary optimization problems. In this method, the semidefinite relaxation is used to reformulate it to a convex binary quadratic program which is solved using mixed integer quadratic programming solvers. We extend this method to random quadratic unconstrained binary optimization problems. We develop a Penal...

Fractional differential equations have extensively used in physics, chemistry as well as engineering fields. Therefore, approximating the solution of differential equations of fractional order is necessary. Consequently, it is essential to approximate the solution of differential equations of fractional order. The piecewise quadratic polynomial function based method has been presented in this p...

Fractional Order Control methods were applied to a three-axis reaction wheels satellite attitude control system. To show the advantages of this method, a comparative study between a Linear Quadratic Regulator and a Fractional Order Control was established through two principal fractional control laws. The aim is to establish an efJicient control law which satisJies a given speczjication and mai...

Consider the nonlinear fractional programming problem max{f(x)lg(x)lxES}, where g(x»O for all XES. Jagannathan and Dinkelbach have shown that the maximum of this problem is equal to ~O if and only if max{f(x)-~g(x) IXES} is 0 for ~=~O. 1 t t Based on this result, we treat here a special case: f(x)=Zx Cx+r x+s, g(X)=~ xtDX+ptX+q and S is a polyhedron, where C is negative definite and D is positi...

A weighted summation of Integral of Time Multiplied Absolute Error (ITAE) and Integral of Squared Controller Output (ISCO) minimization based time domain optimal tuning of fractional-order (FO) PID or PIλDμ controller is proposed in this paper with a Linear Quadratic Regulator (LQR) based technique that minimizes the change in trajectories of the state variables and the control signal. A class ...