On stability of nonlinear nonautonomous discrete fractional Caputo systems

Franco-Pérez, Luis; Fernández‐Anaya, Guillermo; Quezada-Téllez, Luis Alberto

doi:10.1016/j.jmaa.2020.124021

Cited by 19 publications

(5 citation statements)

References 15 publications

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“…The discrete analogues generation for continuous fractional calculus, to deal with fractional difference equations, can be considered an attractive topic [21,24,36,37]. The CDO can be considered as one of those fractional operators that have been significantly studied and used on discrete time scales [38,39]. Here we provide the most relevant definitions and results regarding the CDO.…”

Section: Preliminariesmentioning

confidence: 99%

On the dynamics of a Caputo-like discrete fractional Rössler system: chaos, stabilization and synchronization

2022

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This study examines the dynamics of a novel Caputo-like discrete fractional Rössler system. The dynamics of this discrete fractional system are numerically analyzed using phase portraits, bifurcation diagrams and Lyapunov exponents. The study confirmed the existence of chaos in the proposed system where one scroll chaotic attractors are displayed. Control laws are presented to force the states of the proposed system to converge asymptotically to zero and to exhibit complete synchronization of coupled Caputo-like discrete fractional Rössler systems. Numerical simulations are introduced to illustrate the findings of this study.

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Section: Preliminariesmentioning

confidence: 99%

On the dynamics of a Caputo-like discrete fractional Rössler system: chaos, stabilization and synchronization

2022

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“…Supercapacitors are capable of instant throughput, as a result of their high energy ability. So, in designing, the associated effects of (i) load nature, (ii) load fluctuation, (iii) external environment, and (iv) accidental impact on system stability cannot be ignored [ 177 ]. There are challenges in the design of the power density, energy density, cost, and life of batteries.…”

Section: Challenges and Issues Of Supercapacitors And Batteriesmentioning

confidence: 99%

Review on Comparison of Different Energy Storage Technologies Used in Micro-Energy Harvesting, WSNs, Low-Cost Microelectronic Devices: Challenges and Recommendations

Riaz

Sarker

Saad

et al. 2021

Sensors

111

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This paper reviews energy storage systems, in general, and for specific applications in low-cost micro-energy harvesting (MEH) systems, low-cost microelectronic devices, and wireless sensor networks (WSNs). With the development of electronic gadgets, low-cost microelectronic devices and WSNs, the need for an efficient, light and reliable energy storage device is increased. The current energy storage systems (ESS) have the disadvantages of self-discharging, energy density, life cycles, and cost. The ambient energy resources are the best option as an energy source, but the main challenge in harvesting energy from ambient sources is the instability of the source of energy. Due to the explosion of lithium batteries in many cases, and the pros associated with them, the design of an efficient device, which is more reliable and efficient than conventional batteries, is important. This review paper focused on the issues of the reliability and performance of electrical ESS, and, especially, discussed the technical challenges and suggested solutions for ESS (batteries, supercapacitors, and for a hybrid combination of supercapacitors and batteries) in detail. Nowadays, the main market of batteries is WSNs, but in the last decade, the world’s attention has turned toward supercapacitors as a good alternative of batteries. The main advantages of supercapacitors are their light weight, volume, greater life cycle, turbo charging/discharging, high energy density and power density, low cost, easy maintenance, and no pollution. This study reviews supercapacitors as a better alternative of batteries in low-cost electronic devices, WSNs, and MEH systems.

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“…We use the notation S n−1 ρ = {x ∈ R| x ≤ ρ}. The following definitions were recovered from [24]. Definition 1: Let u ∈ S(N a , R) and v > 0 be given, the v-fractional sum of u is defined by…”

Section: Preliminariesmentioning

confidence: 99%

“…The linear part of ( 12) is given by the term KA[x(t + v − 1)]. The associated linear system is Mittag-Leffler stable by [24,Th. 4] if the matrix KA is negative definite.…”

Section: A a Fractional Proportional Pulse Controlmentioning

confidence: 99%

Controlling Chaos for a Fractional-Order Discrete System

Quezada-Téllez

Franco-Pérez

Fernández‐Anaya

2020

IEEE Open J. Circuits Syst.

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In this article two different controllers for the stabilization of a fractional-order discrete system in the left Caputo discrete delta operator sense are given. The first one acts by a fractional proportional pulse control, the second acts by a fractional feedback control. These controllers are applied to fractional-order chaotic discrete dynamical systems to obtain their stability and also we show a comparison with the integer order dynamical systems stability. Some simulations are presented for the fractional logistic map and the fractional Henon map.INDEX TERMS Caputo delta difference, chaos, discrete fractional calculus, Mittag-Leffler.LUIS ALBERTO QUEZADA-TÉLLEZ received the Ph.D. degree in engineering sciences from Universidad Iberoamericana, where he is also a Professor with the Department of Physics and Mathematics. He has served as a Teacher in several institutions of higher education, both public and private. He is also an Associate Member of the Center for Complexity Sciences, UNAM. He has participated in multiple lectures and has various publications in national and international journals. His areas of research interest include nonlinear systems, chaos theory, control theory, bifurcations, and vehicular traffic models.

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On stability of nonlinear nonautonomous discrete fractional Caputo systems

Cited by 19 publications

References 15 publications

On the dynamics of a Caputo-like discrete fractional Rössler system: chaos, stabilization and synchronization

On the dynamics of a Caputo-like discrete fractional Rössler system: chaos, stabilization and synchronization

Review on Comparison of Different Energy Storage Technologies Used in Micro-Energy Harvesting, WSNs, Low-Cost Microelectronic Devices: Challenges and Recommendations

Controlling Chaos for a Fractional-Order Discrete System

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