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This paper investigates the existence of solutions of the nonlinear fractional differential equation { Du(t) + f(t, u(t),Du(t)) = 0, 0 < t < 1, 3 < α ≤ 4, u(0) = u′(0) = u′′(0) = 0, u(1) = u(ξ), 0 < ξ < 1, where D is the Caputo fractional derivative, β > 0, α− β ≥ 1. The peculiarity of this equation is that the nonlinear term depends on the fractional(More)
In this paper, a model describing dynamics of cellular neural networks with time-varying delays is considered. Without assuming Lipschitz conditions on activation functions, by employing Brouwer's fixed point theorem and applying inequality technique, some new sufficient conditions on the existence, uniqueness and exponential stability of equilibrium point(More)
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