Continuity with Respect to Fractional Order of the Time a Linear Fractional Pseudo-Parabolic Equation

2022 ◽  
Vol 8 (1) ◽  
pp. 137-146
Keyword(s):  
Parabolic Equation ◽  
Fractional Order

scholarly journals Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Guojie Zheng ◽  
M. Montaz Ali
Keyword(s):  
Parabolic Equation ◽  
Bounded Domain ◽  
Fractional Order ◽  
Parabolic Equations ◽  
Positive Measure ◽  
Measure Theory ◽  
Order Parabolic Equation ◽  
Observability Estimate

We establish an observability estimate for the fractional order parabolic equations evolved in a bounded domainΩofℝn. The observation region isF×ω, whereωandFare measurable subsets ofΩand (0,T), respectively, with positive measure. This inequality is equivalent to the null controllable property for a linear controlled fractional order parabolic equation. The building of this estimate is based on the Lebeau-Robbiano strategy and a delicate result in measure theory provided in Phung and Wang (2013).

On Observability of Fractional Order Systems

2009 ◽  
Author(s):  
Jocelyn Sabatier ◽  
Mathieu Merveillaut ◽  
Ludovic Fenetau ◽  
Alain Oustaloup
Keyword(s):  
Parabolic Equation ◽  
State Space ◽  
Fractional Order ◽  
The State ◽  
Fractional Order System ◽  
Order System ◽  
Fractional Order Systems ◽  
System State ◽  
Fractional Systems ◽  
Real State

In this paper, fractional order system observability is discussed. A representation of these systems that involves a classical linear integer system and a system described by a parabolic equation is used to define the system real state and to conclude that the system state cannot be observed. However, it is also shown that the state space like representation usually encountered in the literature for fractional systems, can be used to design Luenberger like observers that permit an estimation of important variables in the system.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

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