Related papers: A Control Oriented Fractional-Order Model of Lithi…
In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…
Interval approaches for the reachability analysis of initial value problems for sets of classical ordinary differential equations have been investigated and implemented by many researchers during the last decades. However, there exist…
We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ Basing on the finite-difference Gr\"{u}nwald-Letnikov…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
Efficient and fast predictor-corrector methods are proposed to deal with nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed…
Cell inconsistency within a lithium-ion battery system poses a significant challenge in maximizing the system operational time. This study presents an optimization-driven active balancing method to minimize the effects of cell inconsistency…
In this paper, we propose a fast second-order approximation to the variable-order (VO) Caputo fractional derivative, which is developed based on $L2$-$1_\sigma$ formula and the exponential-sum-approximation technique. The fast evaluation…
This paper introduces a novel fractional-order chemostat model (FOCM) incorporating Caputo fractional derivative with sliding memory (CFDS) to capture microbial memory effects in biological water treatment, addressing limitations of…
The paper presents two representative classes of Impulsive Fractional Differential Equations defined with generalized Caputo\'s derivative, with fixed lower limit and changing lower limit, respectively. Memory principle is studied and…
In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium…
A parallel numerical simulation algorithm is presented for fractional-order systems involving Caputo-type derivatives, based on the Adams-Bashforth-Moulton (ABM) predictor-corrector scheme. The parallel algorithm is implemented using…
This paper contributes to the design of a fractional order (FO) internal model controller (IMC) for a first order plus time delay (FOPTD) process model to satisfy a given set of desired robustness specifications in terms of gain margin (Am)…
The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
The penetrations of lithium-ion batteries in transport, energy and communication systems are increasing rapidly. A meticulous model applicable for precise in-situ monitoring and convenient online controlling is in sought to bridge the gap…
Currently, the characterization of electric energy storage units used for power system operation and planning models relies on two major assumptions: charge and discharge efficiencies, and power limits are constant and independent of the…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
Standard dynamical systems approaches to economic modeling, such as those deriving the Cobb-Douglas and CES production functions from exponential growth trajectories, typically rely on integer-order differential equations. While effective,…
This study presents a novel high-order numerical method designed for solving the two-dimensional time-fractional convection-diffusion (TFCD) equation. The Caputo definition is employed to characterize the time-fractional derivative. A weak…