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Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels

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Date

2023

Authors

Mohammed, Pshtiwan Othman
Srivastava, Hari Mohan
Baleanu, Dumitru
Al-Sarairah, Eman
Sahoo, Soubhagya Kumar
Chorfi, Nejmeddine

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Abstract

The discrete analysed fractional operator technique was employed to demonstrate positive findings concerning the Atangana-Baleanu and discrete Caputo-Fabrizo fractional operators. Our tests utilized discrete fractional operators with orders between 1<φ<2, as well as between 1<φ<[Formula presented]. We employed the initial values of Mittag–Leffler functions and applied the principle of mathematical induction to ensure the positivity of the discrete fractional operators at each time step. As a result, we observed a significant impact of the positivity of these operators on ∇Q(τ) within Np0+1 according to the Riemann–Liouville interpretation. Furthermore, we established a correlation between the discrete fractional operators based on the Liouville-Caputo and Riemann–Liouville definitions. In addition, we emphasized the positivity of ∇Q(τ) in the Liouville-Caputo sense by utilizing this relationship. Two examples are presented to validate the results.

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Discrete Atangana-Baleanu Fractional Operators, Discrete Caputo-Fabrizo Operators, Discrete Fractional Calculus, Monotonicity And Positivity

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Mohammed, Pshtiwan Othman;...et.al. (2023). "Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels", Journal of King Saud University - Science, Vol35, No.7.

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Journal of King Saud University - Science

Volume

35

Issue

7

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