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

Büyükkaya A., Kesik D., YEŞİL Ü., Öztürk M.

Fractal and Fractional, vol.8, no.12, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 12
  • Publication Date: 2024
  • Doi Number: 10.3390/fractalfract8120724
  • Journal Name: Fractal and Fractional
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Keywords: binary relation, dynamic programming, fixed point, fractional differential equations, partial modular b-metric
  • Yıldız Technical University Affiliated: Yes

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 (Formula presented.), proposing a novel definition for a generalized (Formula presented.) -type Suzuki (Formula presented.) -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.