Analytical Results for Positivity of Discrete Fractional Operators With Approximation of the Domain of Solutions
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Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
Amer inst Mathematical Sciences-aims
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GOLD
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No
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Yes
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Abstract
We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ((CFR)(c0)del F-theta)(t) > -epsilon Lambda(theta - 1) (del F)(c(0) + 1) such that (del F)(c(0) + 1) >= 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.
Description
Mohammed, Pshtiwan/0000-0001-6837-8075; Elattar, Ehab/0000-0002-3966-2584
Keywords
Discrete Fractional Calculus, Caputo-Fabrizio Fractional Difference, Nabla Positivity, Numerical Analysis, numerical analysis, Operator (biology), discrete fractional calculus, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Biochemistry, Gene, Nabla symbol, QA1-939, FOS: Mathematics, caputo-fabrizio fractional difference, Biology, Data mining, Anomalous Diffusion Modeling and Analysis, Omega, Domain (mathematical analysis), Ecology, Applied Mathematics, Physics, Exponential function, Fractional calculus, Pure mathematics, nabla positivity, Computer science, Nonlocal Partial Differential Equations and Boundary Value Problems, Fractional Derivatives, Chemistry, Combinatorics, Modeling and Simulation, Mathematical physics, FOS: Biological sciences, Physical Sciences, Cardinality (data modeling), Repressor, Transcription factor, Type (biology), TP248.13-248.65, Mathematics, Monotonic function, Biotechnology, Difference equations, scaling (\(q\)-differences), Fractional derivatives and integrals, Difference operators, Caputo-Fabrizio fractional difference
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Mohammed, Pshtiwan Othman;...et.al. (2022). "Analytical results for positivity of discrete fractional operators with approximation of the domain of solutions", Mathematical Biosciences and Engineering, Vol.19, No.7, pp.7272-7283.
WoS Q
Q2
Scopus Q
Q2
OpenCitations Citation Count
N/A
Source
Mathematical Biosciences and Engineering
Volume
19
Issue
7
Start Page
7272
End Page
7283
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Scopus : 1
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1
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