Generalized weakly singular Gronwall-type inequalities and their applications to fractional differential equations

Abstract

We propose and prove some new generalized Gronwall-type inequalities with respect to an appropriate function $\psi$. We consider the integral inequalities including not only one integral but also two integrals with doubly singular kernels. We apply these inequalities to study the existence and stability of solution of fractional differential equations with weakly singular sources.