Please use this identifier to cite or link to this item: http://repository.aaup.edu/jspui/handle/123456789/1299
 Title: Monotonicity Analysis of Fractional Proportional Differences Authors: Suwan, Iyad$AAUP$PalestinianOweis, Shahd$AAUP$PalestinianAbusaa, Muayad$AAUP$PalestinianAbdljawad, Thabet$Other$Other Keywords: Riemann-Liouville(RL) fractional proportional di erenceCaputo fractional proportional di erencefractional 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. URI: http://repository.aaup.edu/jspui/handle/123456789/1299 ISSN: https://doi.org/10.1155/2020/4867927 Appears in Collections: Faculty & Staff Scientific Research publications

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