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.