|
| Monotonicity Analysis of Generalized Discrete Fractional Proportional h-Differences with Applications |
| |
| View Full Text View/Add Comment Download reader |
| KeyWord:Monotonicity analysis, $h$-fractional proportional difference, Caputo fractional proportional difference, fractional proportional Mean Value Theorem(MVT) |
| Author Name | Affiliation | | Ammar Qarariyah | Department of Technology, Bethlehem University, Bethlehem, Palestine | | Iyad Suwan | Department of Mathematics and statistics, Arab American University, Zababdeh, Jenin, Palestine | | Muayad Abusaa | Department of Physics, Arab American University, Zababdeh, Jenin, Palestine | | Thabet Abdeljawad | Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India
Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University,Garankuwa, Medusa 0204, South Africa |
|
| Hits: 402 |
| Download times: 699 |
| Abstract: |
| Monotonicity analysis is an important aspect of fractional mathematics. In this paper, we perform a monotonicity analysis for a generalized class of nabla discrete fractional proportional difference on the $h\mathbb{Z}$ scale of time. We first define the sums and differences of order $0< \alpha \leq 1$ on the time scale for a general form of nabla fractional along with Riemann-Liouville $h$-fractional proportional sums and differences. We formulate the Caputo fractional proportional differences and present the relation between them and the fractional proportional differences. Afterward, we introduce and prove the monotonicity results for nabla and Caputo discrete $h$-fractional proportional differences. Finally, we provide two numerical examples to verify the theoretical results along with a proof for a new version of the fractional proportional difference of the mean value theorem on $h\mathbb{Z}$ as an application. |
|
|
|
