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Zbl 1189.26044
Denton, Z.; Vatsala, A.S.
Fractional integral inequalities and applications. (English)
[J] Comput. Math. Appl. 59, No. 3, 1087-1094 (2010). ISSN 0898-1221

Summary: Fractional integral inequality results when $0<q<1$ are developed when the nonlinear term is increasing in $u$ and satisfies a one sided Lipschitz condition. Using the integral inequality result and the computation of the solution of the linear fractional equation of variable coefficients, Gronwall inequality results are established. This yields the results of $q=1$ as a special case. As an application of this, the uniqueness and continuous dependence of the solution on the initial parameters of the nonlinear fractional differential equations are established.

MSC 2000:: *26D15 Inequalities for sums, series and integrals of real functions
26A33 Fractional derivatives and integrals (real functions)
34A08

Keywords: fractional integral inequalities; Gronwall inequality; uniqueness and continuous dependence on parameters

Cited in: Zbl 1222.26013

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