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Title: Fractional ℎ ‐differences with exponential kernels and their monotonicity properties
Authors: Suwan, Iyad$AAUP$Palestinian
Oweis, Shahd$AAUP$Palestinian
Abdeljawad, Thabet$Other$Other
Keywords: nabla h‐discrete exponential kernel
nabla h‐RL fractional difference
nabla h‐CF fractional difference
Issue Date: 25-Jan-2020
Publisher: John Wiley & Sons
Abstract: In this work, the nabla fractional differences of order 0<𝜇<1 with discrete exponential kernels are formulated on the time scale ℎℤ , where 0<ℎ≤1 . Hence, the earlier results obtained in Adv. Differ. Equ., 2017, (78) (2017) are generalized. The monotonicity properties of the ℎ –Caputo‐Fabrizio (CF) fractional difference operator are concluded using its relation with the nabla ℎ –Riemann‐Liouville (RL) fractional difference operator. It is shown that the monotonicity coefficient depends on the step ℎ , and this dependency is explicitly derived. As an application, a fractional difference version of the mean value theorem (MVT) on ℎℤ is proved.
Description: SPECIAL ISSUE PAPER Fractional ℎ ‐differences with exponential kernels and their monotonicity properties Iyad Suwan Shahd Owies Thabet Abdeljawad Mathematical Methods in the Applied Sciences, Early View First published: 25 January 2020
Appears in Collections:Faculty & Staff Scientific Research publications

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