Link theorem and distributions of solutions to uncertain Liouville-Caputo difference equations

Hari Mohan Srivastava; Pshtiwan Othman Mohammed; Juan L. G. Guirao; Y. S. Hamed

doi:10.3934/dcdss.2021083

Article Contents

2022, Volume 15, Issue 2: 427-440. Doi: 10.3934/dcdss.2021083

This issue Previous Article On the random wave equation within the mean square context Next Article A stochastic population model of cholera disease

Link theorem and distributions of solutions to uncertain Liouville-Caputo difference equations

1.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China
3.
Department of Mathematics and Informatics, Azerbaijan University 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
4.
Section of Mathematics, International Telematic University Uninettuno I-00186 Rome, Italy
5.
Department of Mathematics, College of Education University of Sulaimani, Sulaimani, Kurdistan Region, Iraq
6.
Department of Applied Mathematics and Statistics, Technical University of Cartagena Hospital de Marina, ES-30203 Cartagena, Spain
7.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group
8.
Department of Mathematics, Faculty of Science, King Abdulaziz University P.O. Box 80203, Jeddah 21589, Saudi Arabia
9.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

^* Corresponding author
^* Corresponding author

Received: March 2021

Revised: April 2021

Early access: July 2021

Published: February 2022

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Abstract

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 $ \varrho $-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 $ \varrho $-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 $ \varrho $-paths.

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Mathematics Subject Classification: 26A33; 39A60; 81S07; 34A12; 33E12.

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