A Study of Positivity Analysis for Difference Operators in the Liouville–Caputo Setting

Hari Mohan Srivastava, Pshtiwan Othman Mohammed, Juan Luis G. Guirao, Dumitru Baleanu, Eman Al-Sarairah, Rashid Jan

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5 Scopus citations

Abstract

The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a class of Liouville–Caputo difference equations of fractional-order with extremal conditions. Our monotonicity results use difference conditions (Formula presented.) and (Formula presented.) to derive the corresponding relative minimum and maximum, respectively. We find alternative conditions corresponding to the main conditions in the main monotonicity results, which are simpler and stronger than the existing ones. Two numerical examples are solved by achieving the main conditions to verify the obtained monotonicity results.

Original languageBritish English
Article number391
JournalSymmetry
Volume15
Issue number2
DOIs
StatePublished - Feb 2023

Keywords

  • Liouville–Caputo fractional operators
  • monotonicity analysis
  • positivity analysis

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