SPECIAL ISSUE PAPER
Fractional -differences with exponential kernels and their monotonicity properties
Iyad Suwan,
Shahd Owies,
Thabet Abdeljawad,
Corresponding Author
Iyad Suwan
Department of Mathematics and statistics, Arab American University, Jenin, Zababdeh, Palestine
Correspondence
Iyad Suwan, Department of Mathematics and statistics, Arab American University, PO Box 240, Jenin, 13 Zababdeh, Palestine.
Email: [email protected]
Communicated by: T. E. Simos
Search for more papers by this authorShahd Owies
Department of Mathematics and statistics, Arab American University, Jenin, Zababdeh, Palestine
Search for more papers by this authorThabet Abdeljawad
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
Department of Medical Research, China Medical University, Taichung, Taiwan
Search for more papers by this authorIyad Suwan,
Shahd Owies,
Thabet Abdeljawad,
Corresponding Author
Iyad Suwan
Department of Mathematics and statistics, Arab American University, Jenin, Zababdeh, Palestine
Correspondence
Iyad Suwan, Department of Mathematics and statistics, Arab American University, PO Box 240, Jenin, 13 Zababdeh, Palestine.
Email: [email protected]
Communicated by: T. E. Simos
Search for more papers by this authorShahd Owies
Department of Mathematics and statistics, Arab American University, Jenin, Zababdeh, Palestine
Search for more papers by this authorThabet Abdeljawad
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
Department of Medical Research, China Medical University, Taichung, Taiwan
Search for more papers by this authorAbstract
In this work, the nabla fractional differences of order with discrete exponential kernels are formulated on the time scale , where . Hence, the earlier results obtained in Adv. Differ. Equ., 2017, (78) (2017) are generalized. The monotonicity properties of the –Caputo-Fabrizio (CF) fractional difference operator are concluded using its relation with the nabla –Riemann-Liouville (RL) fractional difference operator. It is shown that the monotonicity coefficient depends on the step , and this dependency is explicitly derived. As an application, a fractional difference version of the mean value theorem (MVT) on is proved.
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