On Intuitionistic Fuzzy  N b  Metric Space and Related Fixed Point Results with Application to Nonlinear Fractional Differential Equations.

This manuscript contains several new notions including intuitionistic fuzzy  N b  metric space, intuitionistic fuzzy quasi- S b -metric space, intuitionistic fuzzy pseudo- S b -metric space, intuitionistic fuzzy quasi- N -metric space and intuitionistic fuzzy pseudo  N b  fuzzy metric space. We prove decomposition theorem and fixed-point results in the setting of intuitionistic fuzzy pseudo  N b  fuzzy metric space. Further, we provide several non-trivial examples to show the validity of introduced notions and results. At the end, we solve an integral equation, system of linear equations and nonlinear fractional differential equations as applications. [ABSTRACT FROM AUTHOR]