Comparison Principles of Fractional Differential Equations With Non-Local Derivative and Their Applications
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Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Amer inst Mathematical Sciences-aims
Open Access Color
GOLD
Green Open Access
No
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No
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Top 10%
Abstract
In this paper, we derive and prove a maximum principle for a linear fractional differential equation with non-local fractional derivative. The proof is based on an estimate of the non-local derivative of a function at its extreme points. A priori norm estimate and a uniqueness result are obtained for a linear fractional boundary value problem, as well as a uniqueness result for a nonlinear fractional boundary value problem. Several comparison principles are also obtained for linear and nonlinear equations.
Description
Keywords
Fractional Differential Equations, Maximum Principle, Fractional Derivatives, Financial economics, fractional derivatives, Fractional Differential Equations, Economics, FOS: Political science, Norm (philosophy), A priori estimate, FOS: Law, Epistemology, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Numerical Methods for Singularly Perturbed Problems, QA1-939, FOS: Mathematics, Functional Differential Equations, Boundary value problem, Political science, Anomalous Diffusion Modeling and Analysis, Numerical Analysis, Applied Mathematics, Physics, Fractional calculus, fractional differential equations, A priori and a posteriori, Applied mathematics, FOS: Philosophy, ethics and religion, Fractional Derivatives, Philosophy, maximum principle, Modeling and Simulation, Derivative (finance), Physical Sciences, Nonlinear system, Uniqueness, Law, Mathematics, Nonlinear boundary value problems for ordinary differential equations, Fractional ordinary differential equations, Maximum principles in context of PDEs
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Al-Refai, Mohammed; Baleanu, Dumitru (2021). "Comparison principles of fractional differential equations with non-local derivative and their applications", AIMS Mathematics, Vol. 6, No. 2, pp. 1443-1451.
WoS Q
Q1
Scopus Q
Q1
OpenCitations Citation Count
5
Source
AIMS Mathematics
Volume
6
Issue
2
Start Page
1443
End Page
1451
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Scopus : 5
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Mendeley Readers : 1
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5
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4
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5
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