Certain dynamic iterative scheme families and multi-valued fixed point results

Amjad Ali, Muhammad Arshad, Eskandar Emeer, Hassen Aydi*, Aiman Mukheimer, Kamal Abodayeh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The article presents a systematic investigation of an extension of the developments concerning F-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of F-contractions to the case of non-linear (F, FH )-dynamic-iterative scheme for Branciari Ćirić type-contractions and prove multi-valued fixed point results in controlled-metric spaces. An approximation of the dynamic-iterative scheme instead of the conventional Picard sequence is determined. The paper also includes a tangible example and a graphical interpretation that displays the motivation for such investigations. The work is illustrated by providing an application of the proposed non-linear (F, FH )-dynamic-iterative scheme to the Liouville-Caputo fractional derivatives and fractional differential equations.

Original languageEnglish
Pages (from-to)12177-12202
Number of pages26
JournalAIMS Mathematics
Issue number7
Publication statusPublished - 2022
Externally publishedYes


  • (F, F )-dynamic-iterative scheme
  • Liouville-Caputo fractional differential equation
  • controlled-metric space
  • fixed points


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