A generalized Gronwall inequality and its application to a fractional differential equation

By Haiping Ye, Jianming Gao, Yongsheng Ding. 2007

1,016 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/b80cd7769e944e4d9c53075ab6ae448aba009c5e

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In Applied Mathematics

In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

On stability for nonlinear implicit fractional differential equations (2015, neutral): “4 ([42]).”
Existence of mild solutions for fractional evolution equations with mixed monotone nonlocal conditions (2013, neutral): “([48]).”
Ulam stability and data dependence for fractional differential equations with Caputo derivative (2011, neutral): “[33].”
Stability analysis for nonlinear fractional-order systems based on comparison principle (2014, background): “Lemma 1 [49] Suppose β > 0, c(t) is a nonnegative, nondecreasing function locally integrable on [0, T ) (some T ≤ +∞) and g(t) is a nonnegative, nondecreasing continuous function defined on [0, T ), g(t)≤ M (constant), and suppose u(t) is nonnegative and locally integrable on [0, T ) with”
Some new explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations (2008, background): “9) has been studied in [7], but here we not only have given some new estimates which are not in complicated power series, but also eliminated the nondecreasing condition to function b(t).”
A survey on impulsive fractional differential equations (2016, background): “Introduction Fractional differential equations (FDE) provide an excellent tool for the description of memory and hereditary properties of various materials and processes [5, 10, 21].”
Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach (2009, methodology): “Now, one may apply generalized Gronwall inequality, [24], here, Corollary 3.”
LAPLACE TRANSFORM OF FRACTIONAL ORDER DIFFERENTIAL EQUATIONS (2015, methodology): “The Laplace transform was also used in [6, 7, 13, 14, 15, 21].”
A discrete fractional Gronwall inequality (2012, neutral): “It is our aim in this work to contribute to the development of this theory, presenting the (fundamental) Gronwall inequality (we refer the reader to the works [9, 20] for the continuous Gronwall inequality).”