A second-order difference scheme for the nonlinear time-fractional diffusion-wave equation with generalized memory kernel in the presence of time delay

Alikhanov, Anatoly A.; Asl, Mohammad Shahbazi; Huang, Chengming; Khibiev, Aslanbek

doi:10.1016/j.cam.2023.115515

Cited by 13 publications

(4 citation statements)

References 34 publications

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“…As a first step toward stabilizing the chaotic FO laser mechanism (10), the following steady SS is designed in the initial phase:…”

Section: Design Of the Finite-time Pid Smcmentioning

confidence: 99%

“…Here, selecting κ = 0.99 led to chaotic performance in the FO laser chaotic system (8) [37]. To achieve control of the FO laser chaotic system (10), the parameters of the designed finitetime PID SMC (35) are applied, and Table 1 shows the control parameters. Also, the initial values are x 1 (t) = −5, x 2 (t) = −4, x 3 (t) = 5, and x 4 (t) = 6.…”

Section: Scenariomentioning

confidence: 99%

“…Disciplines such as the medical sciences [4], neural networks [5,6], chemical systems [7], economical systems [8], and emotional sciences [9] have extensively chronicled the substantial role of FO systems. These systems find applications in an array of fields, testifying to their versatility and relevance in modern research and technology [10].…”

Section: Introductionmentioning

confidence: 99%

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A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

Roohi,

Mirzajani,

Basse-O’Connor

2023

Mathematics

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Over the past decade, fractional-order laser chaotic systems have attracted a lot of attention from a variety of fields, including theoretical research as well as practical applications, which has resulted in the development of a number of different system classes. This paper introduces a novel single-input finite-time PID sliding mode control (SMC) technique to stabilize a specific group of unknown 4-dimensional chaotic fractional-order (FO) laser systems. By combining the PID concept with the FO-version of the Lyapunov stability theory, a novel finite-time PID SMC strategy has been developed, which effectively mitigates chaotic behavior in the mentioned unknown 4-dimensional chaotic FO laser system. This method makes use of a characteristic of FO chaotic systems known as boundedness, which is used here. Notably, the control input’s sign function, which is responsible for undesirable chattering, is transformed into the fractional derivative of the control input. This transformation results in a smooth and chattering-free control input, further enhancing the method’s performance. To demonstrate the efficacy of the proposed chattering-free–finite-time PID SMC technique, two numerical scenarios are presented, showcasing its efficient performance in stabilizing the unknown 4-dimensional chaotic FO laser system. These scenarios serve as illustrations of the method’s potential for practical applications.

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“…As a first step toward stabilizing the chaotic FO laser mechanism (10), the following steady SS is designed in the initial phase:…”

Section: Design Of the Finite-time Pid Smcmentioning

confidence: 99%

Section: Scenariomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

Roohi,

Mirzajani,

Basse-O’Connor

2023

Mathematics

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“…Fractional calculus is a branch of mathematics that generalizes the concept of differentiation and integration to fractional orders. It involves operations on functions that are not restricted to integer values of differentiation and integration orders [1,2]. Fractional calculus has found applications in various scientific, engineering, and practical fields.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Fractional-Order Delayed Neural Networks Using Dynamic-Free Adaptive Sliding Mode Control

Roohi,

Zhang,

Taheri

et al. 2023

Fractal Fract

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In this work, a dynamic-free adaptive sliding mode control (adaptive-SMC) methodology for the synchronization of a specific class of chaotic delayed fractional-order neural network systems in the presence of input saturation is proposed. By incorporating the frequency distributed model (FDM) and the fractional version of the Lyapunov stability theory, a dynamic-free adaptive SMC methodology is designed to effectively overcome the inherent chaotic behavior exhibited by the delayed FONNSs to achieve synchronization. Notably, the decoupling of the control laws from the nonlinear/linear dynamical components of the system is ensured, taking advantage of the norm-boundedness property of the states in chaotic systems. The effectiveness of the suggested adaptive-SMC method for chaos synchronization in delayed fractional-order Hopfield neural network systems is validated through numerical simulations, demonstrating its robustness and efficiency. The proposed dynamic-free adaptive-SMC approach, incorporating the FDM and fractional Lyapunov stability theorem, offers a promising solution for synchronizing chaotic delayed FONNSs with input saturation, with potential applications in various domains requiring synchronization of such systems.

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A numerical approach for nonlinear time-fractional diffusion equation with generalized memory kernel

Seal,

Natesan

2023

Numer Algor

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A second-order difference scheme for the nonlinear time-fractional diffusion-wave equation with generalized memory kernel in the presence of time delay

Cited by 13 publications

References 34 publications

A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

Synchronization of Fractional-Order Delayed Neural Networks Using Dynamic-Free Adaptive Sliding Mode Control

A numerical approach for nonlinear time-fractional diffusion equation with generalized memory kernel

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