Abstract
Based on the theory of fractional calculus, the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, a class of Caputo fractional-order BAM neural networks with delays in the leakage terms is investigated in this paper. Some new sufficient conditions are established to guarantee the existence and uniqueness of the nontrivial solution. Moreover, uniform stability of such networks is proposed in fixed time intervals. Finally, an illustrative example is also given to demonstrate the effectiveness of the obtained results.
Highlights
Fractional order calculus was firstly introduced 300 years ago, but it did not attract much attention for a long time since it lack of application background and the complexity
We know that the fractional-order derivative is nonlocal and has weakly singular kernels. It provides an excellent instrument for the description of memory and hereditary properties of dynamical processes where such effects are neglected or difficult to describe to the integer order models
In [13], Chen et al obtained a sufficient condition for uniform stability of a class of fractional-order delayed neural networks
Summary
Fractional order calculus was firstly introduced 300 years ago, but it did not attract much attention for a long time since it lack of application background and the complexity. In [13], Chen et al obtained a sufficient condition for uniform stability of a class of fractional-order delayed neural networks. In [15], Song and Cao considered the existence, uniqueness of the nontrivial solution and uniform stability for a class of neural networks with a fractional-order derivative, by using the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique. Motivated by the above-mentioned works, this paper considers the uniform stability of a class of fractional-order BAM neural networks with delays in the leakage terms described by ( ) ∑.
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