New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular <i>b</i>-Metric Spaces

Abstract

This study explores innovative insights into the realms of dynamic programming and fractional differential equations, situated explicitly within the framework of partial modular b-metric spaces enriched with a binary relation R, proposing a novel definition for a generalized ℷC-type Suzuki R-contraction specific to these spaces. By doing so, we pave the way for a range of relation-theoretical common fixed-point theorems, highlighting the versatility of our approach. To illustrate the practical relevance of our findings, we present a compelling example. Ultimately, this work aims to enrich the existing academic discourse and stimulate further research and practical applications within the field.

Keywords

• fixed point
• partial modular b-metric
• binary relation
• fractional differential equations
• dynamic programming