Some Generalized Neutrosophic Metric Spaces and Fixed Point Results with Applications

This paper contains several novel definitions including neutrosophic Eβ metric space, neutrosophic quasi-Sβ-metric space, neutrosophic pseudo-Sβ-metric space, neutrosophic quasi-E-metric space and neutrosophic pseudo-Eβ-metric space. Further, we present some generalized fixed point results with non-trivial examples and the decomposition theorem in the setting of the neutrosophic pseudo-Eβ-metric space. Moreover, by using the main result, we examine the existence and uniqueness of the solution to an integral equation, a system of linear equations, and nonlinear fractional differential equations.