A study on the solvability of fractional integral equation in a Banach algebra via Petryshyn's fixed point theorem

Halder S., Deepmala D., Tunç C.

Journal of Taibah University for Science, cilt.18, sa.1, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1080/16583655.2024.2410047
  • Dergi Adı: Journal of Taibah University for Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Anahtar Kelimeler: fixed point theory (FPT), fractional functional integral equation (FFIE), fractional integral, Measure of non-compactness (MNC)
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This study focuses on the nonlinear fractional functional integral equation (FFIE) concerning the Riemann-Liouville operator. In certain weaker conditions, the authors demonstrate that the FFIE has a solution, which is defined within the Banach algebra (Formula presented.). Our analysis relies on the Petryshyn's fixed point theorem and the notion of measure of non-compactness (MNC). In addition, our results include numerous authors' work under less restrictive conditions. Furthermore, we provide an illustrative example of fractional functional integral equations to support our proven results.