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Mathematical Biosciences and Engineering

2022, Volume 19, Issue 5: 5120-5133. doi: 10.3934/mbe.2022239
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Positivity and monotonicity results for discrete fractional operators involving the exponential kernel

  • 1.
    Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
  • 2.
    Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
  • 3.
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
  • 4.
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
  • 5.
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy
  • 6.
    Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
  • 7.
    Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

  • Academic Editor: Jesús Martín Vaquero
  • Received: 28 February 2022 Revised: 10 March 2022 Accepted: 16 March 2022 Published: 18 March 2022

  • This work deals with the construction and analysis of convexity and nabla positivity for discrete fractional models that includes singular (exponential) kernel. The discrete fractional differences are considered in the sense of Riemann and Liouville, and the $ \upsilon_{1} $-monotonicity formula is employed as our initial result to obtain the mixed order and composite results. The nabla positivity is discussed in detail for increasing discrete operators. Moreover, two examples with the specific values of the orders and starting points are considered to demonstrate the applicability and accuracy of our main results.

    Citation: Pshtiwan Othman Mohammed, Hari Mohan Srivastava, Sarkhel Akbar Mahmood, Kamsing Nonlaopon, Khadijah M. Abualnaja, Y. S. Hamed. Positivity and monotonicity results for discrete fractional operators involving the exponential kernel[J]. Mathematical Biosciences and Engineering, 2022, 19(5): 5120-5133. doi: 10.3934/mbe.2022239

    Related Papers:

  • This work deals with the construction and analysis of convexity and nabla positivity for discrete fractional models that includes singular (exponential) kernel. The discrete fractional differences are considered in the sense of Riemann and Liouville, and the $ \upsilon_{1} $-monotonicity formula is employed as our initial result to obtain the mixed order and composite results. The nabla positivity is discussed in detail for increasing discrete operators. Moreover, two examples with the specific values of the orders and starting points are considered to demonstrate the applicability and accuracy of our main results.


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