A source identification problem in a time-fractional wave equation with a dynamical boundary condition

2018 ◽  
Vol 75 (12) ◽  
pp. 4337-4354 ◽  
Author(s):  
K. Šišková ◽  
M. Slodička
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Source Identification ◽  
Identification Problem ◽  
Dynamical Boundary Condition ◽  
Fractional Wave Equation ◽  
Time Fractional Wave Equation

scholarly journals On the Fractional Wave Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 874
Author(s):  
Francesco Iafrate ◽  
Enzo Orsingher
Keyword(s):  
Brownian Motion ◽  
Wave Equation ◽  
Wave Equations ◽  
Stable Process ◽  
Space Time ◽  
Probabilistic Interpretation ◽  
Symmetric Stable Process ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Time Fractional Wave Equation

In this paper we study the time-fractional wave equation of order 1 < ν < 2 and give a probabilistic interpretation of its solution. In the case 0 < ν < 1 , d = 1 , the solution can be interpreted as a time-changed Brownian motion, while for 1 < ν < 2 it coincides with the density of a symmetric stable process of order 2 / ν . We give here an interpretation of the fractional wave equation for d > 1 in terms of laws of stable d−dimensional processes. We give a hint at the case of a fractional wave equation for ν > 2 and also at space-time fractional wave equations.

Event-Triggered Boundary Control Strategy for a Time Fractional Wave Equation Subject to Boundary Disturbance

2021 ◽  
Author(s):  
Zhan-Mei Yuan ◽  
Hua-Cheng Zhou
Keyword(s):  
Wave Equation ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Event Time ◽  
Fractional Wave Equation ◽  
Boundary Feedback ◽  
Low Pass ◽  
Boundary Disturbance ◽  
Time Fractional Wave Equation ◽  
Event Triggered

Abstract In this paper, we investigate the event-triggered boundary feedback control problem for an unstable time fractional wave equation with unknown perturbation at the boundary. To cope with the instability of system when there is no disturbance, the backstepping method is adopted to convert the original unstable system into a stable system. An UDE-based estimator based on low-pass filter is proposed to estimate unknown time-varying input disturbance. With the estimation of disturbance, the event-triggered boundary feedback controller is proposed. It is shown that the event-triggered strategy could asymptotically stabilize system and a positive lower bounded of minimum inter-event time is ensured to exclude the Zeno phenomenon.

On a backward problem for nonlinear time fractional wave equations

2021 ◽  
pp. 1-24
Author(s):  
Jia Wei He ◽  
Yong Zhou
Keyword(s):  
Wave Equation ◽  
Regularization Method ◽  
Existence And Uniqueness ◽  
Wave Equations ◽  
Mild Solutions ◽  
Fractional Wave Equation ◽  
Backward Problem ◽  
Fractional Wave Equations ◽  
Time Fractional Wave Equation ◽  
Eigenvalue Expansion

In this paper, we concern with a backward problem for a nonlinear time fractional wave equation in a bounded domain. By applying the properties of Mittag-Leffler functions and the method of eigenvalue expansion, we establish some results about the existence and uniqueness of the mild solutions of the proposed problem based on the compact technique. Due to the ill-posedness of backward problem in the sense of Hadamard, a general filter regularization method is utilized to approximate the solution and further we prove the convergence rate for the regularized solutions.

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