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Relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results

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Date

2022

Authors

Guirao, Juan L. G.
Mohammed, Pshtiwan Othman
Srivastava, Hari Mohan
Baleanu, Dumitru
Abualrub, Marwan S.

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Abstract

In this study, we have presented two new alternative definitions corresponding to the basic definitions of the discrete delta and nabla fractional difference operators. These definitions and concepts help us in establishing a relationship between Riemann-Liouville and Liouville-Caputo fractional differences of higher orders for both delta and nabla operators. We then propose and analyse some convexity results for the delta and nabla fractional differences of the Riemann-Liouville type. We also derive similar results for the delta and nabla fractional differences of Liouville-Caputo type by using the proposed relationships. Finally, we have presented two examples to confirm the main theorems.

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Convexity Analysis, Liouville-Caputo Fractional Difference, Riemann-Liouville Fractional Difference

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Citation

Guirao, Juan L. G.;...et.al. (2022). "Relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results", AIMS Mathematics, Vol.7, No.10, pp.18127-18141.

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AIMS Mathematics

Volume

7

Issue

10

Start Page

18127

End Page

18141