Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators

Kamsing Nonlaopon, Pshtiwan Othman Mohammed, Y. S. Hamed, Rebwar Salih Muhammad, Aram Bahroz Brzo and Hassen Aydi
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Kamsing Nonlaopon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Pshtiwan Othman Mohammed: Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
Y. S. Hamed: Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Rebwar Salih Muhammad: Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
Aram Bahroz Brzo: Department of Physics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
Hassen Aydi: Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, Hammam Sousse 4000, Tunisia

Mathematics, 2022, vol. 10, issue 10, 1-9

Abstract: In this paper, first, we intend to determine the relationship between the sign of Δ c 0 β y ( c 0 + 1 ) , for 1 < β < 2 , and Δ y ( c 0 + 1 ) > 0 , in the case we assume that Δ c 0 β y ( c 0 + 1 ) is negative. After that, by considering the set D ℓ + 1 , θ ⊆ D ℓ , θ , which are subsets of ( 1 , 2 ) , we will extend our previous result to make the relationship between the sign of Δ c 0 β y ( z ) and Δ y ( z ) > 0 (the monotonicity of y ), where Δ c 0 β y ( z ) will be assumed to be negative for each z ∈ N c 0 T : = { c 0 , c 0 + 1 , c 0 + 2 , ⋯ , T } and some T ∈ N c 0 : = { c 0 , c 0 + 1 , c 0 + 2 , ⋯ } . The last part of this work is devoted to see the possibility of information reduction regarding the monotonicity of y despite the non-positivity of Δ c 0 β y ( z ) by means of numerical simulation.

Keywords: discrete fractional calculus; delta fractional difference; monotonicity; numerical approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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