This article introduces a novel Multiplicative-Modular b-Metric Space (MMbMS), which generalizes two Metric Spaces by relaxing the Triangle Inequality. We establish its properties and prove the Banach and Kannan Contraction Theorems with adjusted constants, ensuring their validity in this broader framework. The Banach Contraction Principle is extended to this generalized space, proving its validity under appropriate Contraction Conditions, and its potential applications in solving Integral and Differential Equations are explored.