Some Properties of a Falling Function and Related Inequalities on Green’s Functions

Asymmetry plays a significant role in the transmission dynamics in novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed discrete models that incorporate different symmetry developmental stages. This paper introduces a Taylor m...

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Bibliographic Details
Published in:Symmetry (Basel) 2024-03, Vol.16 (3), p.337
Main Authors: Mohammed, Pshtiwan Othman, Agarwal, Ravi P., Yousif, Majeed A., Al-Sarairah, Eman, Mahmood, Sarkhel Akbar, Chorfi, Nejmeddine
Format: Article
Language:English
Subjects:
Asymmetry
Boundary value problems
Calculus
falling function
Fractional calculus
Green's functions
Inequalities
Lyapunov inequalities
Mathematical analysis
Riemann–Liouville operator
Upper bounds
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Summary:Asymmetry plays a significant role in the transmission dynamics in novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed discrete models that incorporate different symmetry developmental stages. This paper introduces a Taylor monomial falling function and presents some properties of this function in a delta fractional model with Green’s function kernel. In the deterministic case, Green’s function will be non-negative, and this shows that the function has an upper bound for its maximum point. More precisely, in this paper, based on the properties of the Taylor monomial falling function, we investigate Lyapunov-type inequalities for a delta fractional boundary value problem of Riemann–Liouville type.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym16030337