An accurate state of charge (SOC) estimation is the basis of the Battery Management System (BMS). In this paper, a new estimation method which considers fractional calculus is proposed to estimate the lithium battery state of charge. Firstly, a modified second-order RC model based on fractional calculus theory is developed to model the lithium battery characteristics. After that, a pulse charac...

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the ...

The widely used backpropagation algorithm based on stochastic gradient descent suffers from typically slow convergence to either local or global minimum error. This backpropagation algorithm bears great resemblance to a classic proportional integral derivative (PID) control system. Fractional calculus shows promise for improving stability and response in feedback control through the use of non-...

In this article, we propose the definition of one parameter matrix Mittag-Leffler functions of fractional nabla calculus and present three different algorithms to construct them. Examples are provided to illustrate the applicability of suggested algorithms.

In this paper, it is considered that chaos synchronization of Chen fractional order time-delay chaotic systems and its application in secure communication. By use of the fractional calculus techniques, we find that chaos exists in the fractional order Chen system with time delays when the order is less than 3. Firstly, based on the Laplace transform theory, the conditions for achieving synchron...

Traditional continuous-time filters are of integer order. However, using fractional calculus, filters may also be represented by the more general fractional-order differential equations in which case integer-order filters are only a tight subset of fractional-order filters. In this work, we show that low-pass, high-pass, band-pass, and all-pass filters can be realized with circuits incorporatin...

Abstract Fractional calculus is a branch of classical mathematics, which deals with the generalization of operations of differentiation and integration to fractional order. Such a generalization is not merely a mathematical curiosity but has found applications in various fields of physical sciences. In this paper, we review the definitions and properties of fractional derivatives and integrals,...

Aiming at the characteristics of permanent magnet synchronous motor (PMSM) such as strong coupling and nonlinearity, we propose a fractional-order control scheme for the speed control of PMSM system based on the analysis of the fractional calculus theory. The simulation is conducted by using Matlab / Simulink. Simulation results indicate that the fractional-order PI controller can improve the d...

We numerically investigate the dynamical behavior of the fractional-order Chua’s system. By utilizing the multistep generalized differential transform method MSGDTM , we find that the fractional-order Chua’s system with “effective dimension” less than three can exhibit chaos as well as other nonlinear behavior. Numerical results are presented graphically and reveal that the multistep generalize...