Application of fixed point theory to synaptic delay differential equations in neural networks

The objective of this research is to propose a new concept known as rational ($ \alpha \eta $-$ \psi) $-contractions in the framework of $ \mathcal{F} $-metric spaces and to establish several fixed point theorems. These theorems help to generalize and unify various established fixed point results from the existing literature. To demonstrate the practical effectiveness of our approach, we provide a significant example that confirms our findings. In addition, we introduce a generalized multivalued ($ \alpha $-$ \psi) $-contraction concept in $ \mathcal{F} $-metric spaces and use it to prove fixed point theorems specifically designed for multivalued mappings. To demonstrate the practical utility of our findings, we apply our main results to the solution of synaptic delay differential equations in neural networks.