In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

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...

This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.

This paper analyses the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional-order dynamics is illustrated using the Nyquist plot and the results are compared with those of standard models.

In this paper, we study the controllability of linear and nonlinear fractional damped dynamical systems, which involve fractional Caputo derivatives, with different order in finite dimensional spaces using the Mittag-Leffler matrix function and the iterative technique. A numerical example is provided to illustrate the theory.

We propose the two formalisms for obtaining the noncommutative spacetime in a magnetic field. One is the first-order formalism and the other is the second-order formalism. Although the noncommutative spacetime is realized manifestly in the first-order formalism, the second-order formalism would be more useful for calculating the physical quantities in the noncommutative geometry than the first-...