A Gronwall Inequality Via the Generalized Proportional Fractional Derivative With Applications
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Date
2019
Journal Title
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Publisher
Springer
Open Access Color
GOLD
Green Open Access
No
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No
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Top 1%
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Top 10%
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Top 10%
Abstract
In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its features. As an application, we accommodate the newly defined derivative to prove the uniqueness and obtain a bound in terms of Mittag-Leffler function for the solutions of a nonlinear delay proportional fractional system. An example is presented to demonstrate the applicability of the theory.
Description
Jarad, Fahd/0000-0002-3303-0623; Sudsutad, Weerawat/0000-0002-6762-813X; Alzabut, Prof. Dr. Jehad/0000-0002-5262-1138
Keywords
Proportional Gronwall Inequality, Uniqueness Of Solution, Delay Proportional Fractional System, Bound For The Solution, Financial economics, Bound for the solution, Economics, Uniqueness of solution, Evolutionary biology, Matrix Inequalities and Geometric Means, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Delay proportional fractional system, Proportional Gronwall inequality, QA1-939, FOS: Mathematics, Biology, Anomalous Diffusion Modeling and Analysis, Applied Mathematics, Physics, Fractional calculus, Pure mathematics, Applied mathematics, Gronwall's inequality, Fractional Derivatives, Inequality, Function (biology), Modeling and Simulation, Derivative (finance), Physical Sciences, Nonlinear system, Uniqueness, Mathematics, Mittag-Leffler functions and generalizations, Fractional derivatives and integrals, bound for the solution, proportional Gronwall inequality, delay proportional fractional system, Inequalities for sums, series and integrals, uniqueness of solution
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Alzabut, Jehad...et al. (2019). "A Gronwall inequality via the generalized proportional fractional derivative with applications", Journal of Inequalities and Applications.
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OpenCitations Citation Count
54
Source
Journal of Inequalities and Applications
Volume
2019
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CrossRef : 43
Scopus : 79
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