Monotonicity Results for Nabla Riemann–Liouville Fractional Differences

Pshtiwan Othman Mohammed, Hari Mohan Srivastava, Dumitru Baleanu, Rashid Jan and Khadijah M. Abualnaja
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Pshtiwan Othman Mohammed: Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Dumitru Baleanu: Department of Mathematics, Cankaya University, Ankara 06530, Turkey
Rashid Jan: Department of Mathematics, University of Swabi, Swabi 23430, KPK, Pakistan
Khadijah M. Abualnaja: Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Mathematics, 2022, vol. 10, issue 14, 1-14

Abstract: Positivity analysis is used with some basic conditions to analyse monotonicity across all discrete fractional disciplines. This article addresses the monotonicity of the discrete nabla fractional differences of the Riemann–Liouville type by considering the positivity of ∇ b 0 R L θ g ( z ) combined with a condition on g ( b 0 + 2 ) , g ( b 0 + 3 ) and g ( b 0 + 4 ) , successively. The article ends with a relationship between the discrete nabla fractional and integer differences of the Riemann–Liouville type, which serves to show the monotonicity of the discrete fractional difference ∇ b 0 R L θ g ( z ) .

Keywords: discrete fractional calculus; discrete nabla Riemann–Liouville fractional differences; monotonicity analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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