Heterogeneous Multiagent Systems With Different Fractional Order: An Experience-Based Fusion Controller

Chen, Yiwen; Wen, Guoguang; Rahmani, Ahmed; Huang, Tingwen

doi:10.1109/tcsii.2022.3162697

Cited by 10 publications

(2 citation statements)

References 22 publications

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“…Thus, we know ||χ t || + ||ρD 2−α 0,t χ|| + ||I α−1 0,t χ|| ≤ CN −m according to (4). Moreover, we have…”

Section: Stability and Convergence Analysismentioning

confidence: 94%

“…Fractional differential equations (FDEs), as the evolution of integral differential equations, can more precisely describe phenomena with sophisticated dynamics [1][2][3][4]. In the past few decades, FDEs have been investigated by a number of scholars because they have practical applications in various fields, such as relativistic quantum mechanics [5], hydromechanics [6], neuroscience [7], and materials science [8].…”

Section: Introductionmentioning

confidence: 99%

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A Fast θ Scheme Combined with the Legendre Spectral Method for Solving a Fractional Klein–Gordon Equation

Li,

Xu,

Liu

et al. 2023

Fractal Fract

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In the current work, a fast θ scheme combined with the Legendre spectral method was developed for solving a fractional Klein–Gordon equation (FKGE). The numerical scheme was provided by the Legendre spectral method in the spatial direction, and for the temporal direction, a θ scheme of order O(τ2) with a fast algorithm was taken into account. The fast algorithm could decrease the computational cost from O(M2) to O(MlogM), where M denotes the number of time levels. In addition, correction terms could be employed to improve the convergence rate when the solutions have weak regularity. We proved theoretically that the scheme is unconditionally stable and obtained an error estimate. The numerical experiments demonstrated that our numerical scheme is accurate and efficient.

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“…Thus, we know ||χ t || + ||ρD 2−α 0,t χ|| + ||I α−1 0,t χ|| ≤ CN −m according to (4). Moreover, we have…”

Section: Stability and Convergence Analysismentioning

confidence: 94%