Abstract
This manuscript contains several new notions including intuitionistic fuzzy Nb metric space, intuitionistic fuzzy quasi-Sb-metric space, intuitionistic fuzzy pseudo-Sb-metric space, intuitionistic fuzzy quasi-N-metric space and intuitionistic fuzzy pseudo Nb fuzzy metric space. We prove decomposition theorem and fixed-point results in the setting of intuitionistic fuzzy pseudo Nb 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.
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