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In this manuscript, a class of fractional delay differential equation is considered under multi-point boundary conditions. Two important aspects including existence theory and stability results are developed. For the concerned results prior estimate method and some results of nonlinear analysis are used. By giving a pertinent example the main results are justified. [ABSTRACT FROM AUTHOR]

We develop a delay differential equation model for the interactive wild and sterile mosquitoes. Different from the existing modelling studies, we assume that only those sexually active sterile mosquitoes play a role for the interactive dynamics. We consider the cases where the release amount is either constant or described by a given function of time. For the constant releases, we establish a threshold of releases to determine whether the wild mosquito suppression succeeds or fails. We study the existence and stability of the model equilibria. When the releases are described by given functions, the trivial equilibrium is no longer globally but locally uniformly asymptotically stable if the amount of releases is below the threshold whereas it is still globally uniformly asymptotically stable if the release amount is above the threshold. Numerical examples demonstrating the model dynamical features and brief discussions of our findings are also provided. [ABSTRACT FROM AUTHOR]