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On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically

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2023

Authors

Baleanu, Dumitru
Mohammed, Pshtiwan Othman
Srivastava, Hari Mohan
Al-Sarairah, Eman
Abdeljawad, Thabet
Hamed, Y.S.

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Abstract

In this paper, we focus on the analytical and numerical convexity analysis of discrete delta Riemann–Liouville fractional differences. In the analytical part of this paper, we give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. We establish a formula for the Δ 2, which will be useful to obtain the convexity results. We examine the correlation between the positivity of (w0RLΔαf)(t) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of (2 , 3 ) , Hk,ϵ and Mk,ϵ. The decrease of these sets allows us to obtain the relationship between the negative lower bound of (w0RLΔαf)(t) and convexity of the function on a finite time set Nw0P:={w0,w0+1,w0+2,…,P} for some P∈Nw0:={w0,w0+1,w0+2,…}. The numerical part of the paper is dedicated to examinin the validity of the sets Hk,ϵ and Mk,ϵ for different values of k and ϵ. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.

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Analytical And Numerical Results, Convexity Analysis, Discrete Delta Riemann–Liouville Fractional Difference, Negative Lower Bound

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Baleanu, D.;...et.al. (2023). "On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically", Journal of Inequalities and Applications, Vol.2023, no.1.

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Journal of Inequalities and Applications

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2023

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1

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