Generalized weakly singular Gronwall-type inequalities and their applications to fractional differential equations (Q1983199)

In this paper, the author obtains some new generalized Gronwall-type inequalities with respect to an appropriate function. A weak-type singular Gronwall-type inequality involving an appropriate function was given. Moreover, a Gronwall-type inequality in which the right-hand side includes two integrals with doubly singular kernels was established. Finally, some applications of the above results were presented to investigate the existence and stability of solutions of fractional differential equations involving \(\psi\)-Caputo and \(\psi\)-Hilfer fractional derivatives.