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, cilt.8, sa.12, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 12
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/fractalfract8120724
  • Dergi Adı: Fractal and Fractional
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Anahtar Kelimeler: binary relation, dynamic programming, fixed point, fractional differential equations, partial modular b-metric
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.