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Analytical results for positivity of discrete fractional operators with approximation of the domain of solutions

Math Biosci Eng. 2022 May 18;19(7):7272-7283. doi: 10.3934/mbe.2022343.


We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where $ left({}_{{c_0}}^{C{F_R}}nabla^{theta} mathtt{F}right)(t) > -epsilon, Lambda(theta-1), bigl(nabla mathtt{F}bigr)(c_{0}+1) $ such that $ bigl(nabla mathtt{F}bigr)(c_{0}+1)geq 0 $ and $ epsilon > 0 $. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of $ epsilon $ and $ theta $.

PMID:35730306 | DOI:10.3934/mbe.2022343

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