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Fractional h ‐differences with exponential kernels and their monotonicity properties
Author(s) -
Suwan Iyad,
Owies Shahd,
Abdeljawad Thabet
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6213
Subject(s) - mathematics , monotonic function , nabla symbol , exponential function , operator (biology) , fractional calculus , mathematical analysis , pure mathematics , omega , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene
In this work, the nabla fractional differences of order 0 < μ < 1 with discrete exponential kernels are formulated on the time scale h Z , 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 h Z is proved.