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In this paper, we investigate the fractional hybrid integro-differential equations with Dirichlet boundary conditions. We first prove the existence of a unique solution for the equation using a fixed point technique. Our main goal is to obtain the best approximation using optimal controllers. After s...
Definition Namespace: Microsoft.VisualStudio.RpcContracts.Solution Assembly: Microsoft.VisualStudio.RpcContracts.dll Package: Microsoft.VisualStudio.RpcContracts v17.12.12 C++ public:staticbooloperator!=(Microsoft::VisualStudio::RpcContracts::Solution::OpenCodeContainersState ^ left, Microsoft...
Zhou and Han [17] establish the upper-bound lifespan estimate of the solution to the variable-coefficient wave equation with f(u,ut)=|ut|p by deriving an ordinary differential inequality. Han and Zhou [6] employ the Kato lemma to present the blow-up dynamics for problem (1.3) with f(...
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With an initial interest in applications in mind, we start off with the introduction of some operators related to vector calculus. 6.1 First Order Sobolev Spaces Throughout this section let Ω⊆Rd be an open set. Definition We define gradc:Cc∞(Ω)⊆L2(Ω)→L2(Ω)dϕ↦(∂j...
In this paper, we focus on the problem of periodic solutions to differential equations on time scales. Let us briefly review the research progress on the above issues. In 2007, Kaufmann and Raffoul [9] introduced a new definition of periodic time scale and studied nonlinear neutral dynamic equa...
This paper is devoted to investigating the initial boundary value problem for a semilinear wave equation with strong damping and scattering damping on an exterior domain. By introducing suitable multipliers and applying the test-function technique togeth
Definition 2.1 If C⊆OA is closed under composition and contains the projectionsei(n):(x1,…,xn)↦xi for all 1≤i≤n∈N, then C is said to be a clone (notation: C≤OA). For an arbitrary set F of operations on A, there is a least clone [F] containing F, called the clone...