Webb, Jeffrey2022-10-252022-10-252021-09-20Webb, J. R. L. (2021). A fractional Gronwall inequality and the asymptotic behaviour of global solutions of Caputo fractional problems. <i>Electronic Journal of Differential Equations, 2021</i>(80), pp. 1-22.1072-6691https://hdl.handle.net/10877/16238We study the asymptotic behaviour of global solutions of some nonlinear integral equations related to some Caputo fractional initial value problems. We consider problems of fractional order between 0 and 1 and of order between 1 and 2, each in two cases: when the nonlinearity depends only on the function, and when the nonlinearity also depends on fractional derivatives of lower order. Our main tool is a new Gronwall inequality for integrals with singular kernels, which we prove here, and a related boundedness property of a fractional integral of an L1[0, ∞) function.Text22 pages1 file (.pdf)enAttribution 4.0 InternationalFractional derivativesAsymptotic behaviourGronwall inequalityWeakly singular kernelArticle