Weakly singular Gronwall inequalities and applications to fractional differential equations

By J. R. L. Webb. Journal of Mathematical Analysis and Applications, 2019

102 citations recorded by the source corpus.

Abstract We obtain some new Gronwall type inequalities which are applicable to some weakly singular Volterra integral equations similar to the ones first studied by D. Henry. The main interest is that we consider cases with a double singularity and we obtain explicit L ∞ bounds rather than L 1 bounds. Furthermore our bounds involve the exponential function and not the Mittag-Leffler function as in some previous works. We give applications to some Volterra integral equations with a doubly singular kernel that arise from Caputo fractional differential equations where, as opposed to previous papers, we have a singularity in the nonlinearity.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/7d34e500ed97e4e04fd1fdf48a034138314c952b

Citations in the corpus

• Semilinear Caputo time-fractional pseudo-parabolic equations (2021, unknown): “(See [58]) Let A,B, δ, δ′ be non-negative constants and δ, δ′ < 1.”