In this manuscript, a numerical method based on the conjunction of Paraskevopoulos's algorithm and operational matrices is developed to solve numerically multi-order linear nonlinear fractional differential equations. By means conjunction, problem decomposed into system equations order which are then solved by employing approach. The accuracy efficiency examined taking some examples. addition, ...

This paper proposes an optimized control policy over type one diabetes. Type one diabetes is taken into consideration as a nonlinear model (Augmented Minimal Model), which is implemented in MATLAB-SIMULINK. This Model is developed in consideration of the patient's conditions. There are some uncertainties in the regarded model due to factors such as blood glucose concentration, daily meals or su...

Necessary and sufficient conditions are explored for the asymptotic stability instability of linear two-dimensional autonomous systems fractional-order differential equations with Caputo derivatives. Fractional-order-dependent fractional-order-independent properties fully characterized, in terms main diagonal elements systems' matrix, as well its determinant.

The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by fractional-order differential equation. First, as an example of such system, viscoelastically damped structure is selected. Second, LQR designed for in which terms are contained the equation motion. An iteration-based method solving algebraic Riccati proposed order obtain feedback gains LQR. ...

Addition formulas for theta functions of arbitrary order are shown and applied to the theoretical understanding of the fractional quantum Hall effect in a multi-layer two-dimensional many-electron system under periodic conditions.