Extension of lower and upper solutions approach for generalized nonlinear fractional boundary value problems

Batool A., Talib I., Riaz M. B., Tunç C.

Arab Journal of Basic and Applied Sciences, cilt.29, sa.1, ss.249-256, 2022 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/25765299.2022.2112646
  • Dergi Adı: Arab Journal of Basic and Applied Sciences
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.249-256
  • Anahtar Kelimeler: Antiperiodic boundary conditions, Caputo fractional derivative, Fractional differential equations, Nonlinear boundary conditions, Periodic boundary conditions, Upper and Lower solutions
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

© 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.Our main concern in this study is to present the generalized results to investigate the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. The framework of the presented results relies on the lower and upper solutions approach which allows us to ensure the existence of solutions in a sector defined by well-ordered coupled lower and upper solutions. It is worth mentioning that the presented results unify the existence criteria of certain problems which were treated on a case-by-case basis in the literature. Two examples are supplied to support the results.