Please use this identifier to cite or link to this item:
Title: Monotonicity Analysis of Fractional Proportional Differences
Authors: Suwan, Iyad$AAUP$Palestinian
Oweis, Shahd$AAUP$Palestinian
Abusaa, Muayad$AAUP$Palestinian
Abdljawad, Thabet$Other$Other
Keywords: Riemann-Liouville(RL) fractional proportional di erence
Caputo fractional proportional di erence
fractional proportional Mean Value Theorem(MVT)
Issue Date: 1-May-2020
Publisher: Hindawi
Series/Report no.: 4867927;
Abstract: In this work, the nabla discrete new Riemann-Liouville and Caputo fractional proportional differences of order $0<\varepsilon<1$ on the time scale $ \mathbb{Z} $ are formulated. The differences and summations of discrete fractional proportional are detected on $\mathbb{Z}$, and the fractional proportional sums associated to $ \left( ^{R} _{c} \nabla ^{\varepsilon , \rho} \chi \right)(z) $ with order $0<\varepsilon<1$ are defined. The relation between nabla Riemann-Liouville and Caputo fractional proportional differences is derived. The monotonicity results for the nabla Caputo fractional proportional difference are proved; specifically, if $( _{c-1} ^{R} \nabla ^{\varepsilon , \rho} \chi )(z) > 0 $ then $\chi(z)$ is $ \varepsilon \rho \ -$increasing, and if $\chi(z)$ is strictly increasing on $ \mathbb{N}_{c} $ and $\chi(c)>0$, then ($_{c-1} ^{R} \nabla ^{\varepsilon , \rho } \chi )(z) > 0$. As an application of our findings, a new version of fractional proportional difference of the Mean Value Theorem(MVT) on $\mathbb{Z}$ is proved.
Appears in Collections:Faculty & Staff Scientific Research publications

Files in This Item:
File Description SizeFormat 
Iyad Suwan Hindawi.pdf777.82 kBAdobe PDFThumbnail

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Admin Tools