Analysis and analytical solution of incommensurate fuzzy fractional nabla difference systems in neural networks

Uncertain incommensurate fractional nabla difference systems (IFDSs) in recurrent neural networks (RNNs) are analyzed using fuzzy number theory to address input uncertainties. Fuzzy number theory and its operations are reinvestigated, and the H-differenceable concept is introduced. The existence of a unique H-differenceable solution for incommensurate RNNs is proved. A recursive algorithm is proposed to obtain fuzzy solutions. Illustrative examples with 2-dimensional IFDSs are provided to validate the framework for integrating fractional calculus, fuzzy dynamics and incommensurate RNNs.