Nonlinear Gronwall–Bellman Type Inequalities and Their Applications
نویسندگان
چکیده
منابع مشابه
Nonlinear Gronwall–Bellman Type Inequalities and Their Applications
In this paper, some nonlinear Gronwall–Bellman type inequalities are established. Then, the obtained results are applied to study the Hyers–Ulam stability of a fractional differential equation and the boundedness of solutions to an integral equation, respectively.
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In this paper we present some new generalized retarded nonlinear integral inequalities of Gronwall-Bellman type. Using integral and differential skills, some new results which provide explicit bounds on unknown functions in integral inequalities are investigated. Some applications are also presented to illustrate the usefulness of some of our results.
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Gronwall-Bellman inequalities and their various linear and nonlinear generalizations play very important roles in the discussion of existence, uniqueness, continuation, boundedness, and stability properties of solutions of differential equations and difference equations. The literature on such inequalities and their applications is vast. For example, see 1–12 for continuous cases, and 13–20 for...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2017
ISSN: 2227-7390
DOI: 10.3390/math5020031