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Barbu and Sritharan [13] established the existence and uniqueness of weak solutions to the Navier-Stokes equations with the forcing term containing delay in 2003.
The purpose of our manuscript is to extend the results in Theorem 1 and Theorem 2 and obtain a new discrete q-fractional version of the Gronwall inequality valid for nonlinear systems containing delay arguments.
In 2014, García-Luengo et al. [20] studied the 2D Navier-Stokes system with the convective term and external force both containing delay and proved the existence of pullback attractors.
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Together with (1.1), we consider a system with the terms containing delays omitted (15).
The asymptotic behavior of the solutions of the first-order differential equation containing delays is studied with,,,.
Together with (1), we consider a system with the terms containing delays omitted x ( k + 1 ) = A x ( k ) (5). and the characteristic equation det ( A − λ I ) = 0. (6).
Additionally, if the dynamic constraints or the performance index contain delay arguments, we are faced with a delay fractional optimal control problem (DFOCP).
In addition, if the system contains delay both in its states and in the derivatives of its states, then the system is usually called a neutral type delay system.
Observing the ambiguity function of signals, the signal characteristic, which not only includes the orthogonality and energy distribution of communication signals but also contains delay ambiguity and Doppler ambiguity of radar signals, can be obtained.
This paper focuses on the problem of H∞-control design for linear systems with multiple time-delays, in which the controlled output contains delayed states and disturbance input.
This is why the code can contain delayed signals, i.e., signals produced (or inputs) in a previous data processing, which are used as operands during the current execution of the code (for instance, A[ i][ j] @3 means an array reference produced three time iterations in the past).
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