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Monotonicity Results for Nabla Riemann–Liouville Fractional Differences

Author

Listed:
  • 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
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy)

  • Dumitru Baleanu

    (Department of Mathematics, Cankaya University, Ankara 06530, Turkey
    Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
    Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut 11022801, Lebanon)

  • 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)

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 ) .

Suggested Citation

  • Pshtiwan Othman Mohammed & Hari Mohan Srivastava & Dumitru Baleanu & Rashid Jan & Khadijah M. Abualnaja, 2022. "Monotonicity Results for Nabla Riemann–Liouville Fractional Differences," Mathematics, MDPI, vol. 10(14), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2433-:d:861140
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    References listed on IDEAS

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    1. Abdeljawad, Thabet & Baleanu, Dumitru, 2017. "Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 106-110.
    2. Thabet Abdeljawad & Ferhan M. Atici, 2012. "On the Definitions of Nabla Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, October.
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