A fractional Gronwall inequality and the asymptotic behaviour of global solutions of Caputo fractional problems
Texas State University, Department of Mathematics
We 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.
Fractional derivatives, Asymptotic behaviour, Gronwall inequality, Weakly singular kernel
Webb, 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.