A Generalized Q-Fractional Gronwall Inequality and Its Applications To Nonlinear Delay Q-Fractional Difference Systems
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Date
2016
Journal Title
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Volume Title
Publisher
Springeropen
Open Access Color
GOLD
Green Open Access
No
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No
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Top 10%
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Top 10%
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Top 10%
Abstract
In this paper, we state and prove a new discrete q-fractional version of the Gronwall inequality. Based on this result, a particular version expressed by means of the q-Mittag-Leffler function is provided. To apply the proposed results, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo q-fractional difference system. We examine our results by providing a numerical example.
Description
Abdeljawad, Thabet/0000-0002-8889-3768; Alzabut, Prof. Dr. Jehad/0000-0002-5262-1138
Keywords
Generalized Q-Fractional Gronwall Inequality, Delay Q-Fractional Difference System, Uniqueness Of Solution, Estimate For The Solution, estimate for the solution, Evolutionary biology, delay q-fractional difference system, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Orthogonal Polynomials, QA1-939, FOS: Mathematics, Discrete Mathematics and Combinatorics, Biology, Anomalous Diffusion Modeling and Analysis, Applied Mathematics, Physics, Applied mathematics, Gronwall's inequality, Fractional Derivatives, Inequality, Function (biology), Modeling and Simulation, Physical Sciences, Nonlinear system, generalized q-fractional Gronwall inequality, Uniqueness, Analysis, Mathematics, uniqueness of solution, \(q\)-Mittag-Leffler function, Difference equations, scaling (\(q\)-differences), Mittag-Leffler functions and generalizations, generalized \(q\)-fractional Gronwall inequality, Other analytical inequalities, numerical example, nonlinear delay Caputo \(q\)-fractional difference system
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Abdeljawad, T., Alzabut, J., Baleanu, D. (2016). A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems. Journal Of Inequalities Applications. http://dx.doi.org/ 10.1186/s13660-016-1181-2
WoS Q
Q1
Scopus Q
Q2
OpenCitations Citation Count
41
Source
Journal of Inequalities and Applications
Volume
2016
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CrossRef : 4
Scopus : 60
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SCOPUS™ Citations
60
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Web of Science™ Citations
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2
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