New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular b-Metric Spaces - Buyukkaya, Abdurrahman; Kesik, Dilek; Yesil, Ulku; Ozturk, Mahpeyker (MDPI, 2024)
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 gimel C-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; FIXED-POINT THEOREMS; CONTRACTION; Mathematics