Open AccessLink theorem and distributions of solutions to uncertain Liouville-Caputo difference equations
Author(s) -
H. M. Srivástava,
Pshtiwan Othman Mohammed,
Juan Luis García Guirao,
Y. S. Hamed
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021083
Subject(s) - mathematics , uniqueness , comparison theorem , pure mathematics , discrete mathematics , combinatorics , mathematical analysis
We consider a class of initial fractional Liouville-Caputo difference equations (IFLCDEs) and its corresponding initial uncertain fractional Liouville-Caputo difference equations (IUFLCDEs). Next, we make comparisons between two unique solutions of the IFLCDEs by deriving an important theorem, namely the main theorem. Besides, we make comparisons between IUFLCDEs and their \begin{document}$ \varrho $\end{document} -paths by deriving another important theorem, namely the link theorem, which is obtained by the help of the main theorem. We consider a special case of the IUFLCDEs and its solution involving the discrete Mittag-Leffler. Also, we present the solution of its \begin{document}$ \varrho $\end{document} -paths via the solution of the special linear IUFLCDE. Furthermore, we derive the uniqueness of IUFLCDEs. Finally, we present some test examples of IUFLCDEs by using the uniqueness theorem and the link theorem to find a relation between the solutions for the IUFLCDEs of symmetrical uncertain variables and their \begin{document}$ \varrho $\end{document} -paths.