In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

‎in this paper‎, ‎we introduce fractional-order into a model of hiv-1 infection of cd4^+ t--cells‎. ‎we study the effect of ‎the changing the average number of viral particles $n$ with different sets of initial conditions on the dynamics of‎ ‎the presented model‎. ‎ ‎the nonstandard finite difference (nsfd) scheme is implemented‎ ‎to study the dynamic behaviors in the fractional--order hiv-1‎‎i...

In this paper, a new tool that is fractional Fourier Transform is introduced to 3D model retrieval. And we propose a 3D model descriptor based on 3D factional Fourier transform. Fractional Fourier transform is a general format of Fourier transform, and add a variables that is order. Our approach is based on volume. The first step of the approach is that voxelize these 3D models. A coarse voxeli...

Quadrotor systems are becoming increasingly popular in various applications due to their maneuverability and versatility. Controlling these accurately is crucial ensure stability safety. This research paper proposes the implementation of two advanced controllers with integer fractional order quadrotor systems. The purpose study enhance control performance, robustness, accuracy system, highlight...

Abstract In this paper, an online optimization approach of a fractional-order PID controller based on actor-critic algorithm (FOPID-FOAC) is proposed. The proposed FOPID-FOAC scheme exploits the advantages FOPID and FOAC approaches to improve performance nonlinear systems. built by developing FO-based learning for neural network with adaptive rates. Moreover, FO rectified linear unit (RLU) intr...