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Fractional integral inequalities and applications. (English) Zbl 1189.26044

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:

26D15 Inequalities for sums, series and integrals
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
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