Positive solution of nonlinear fractional differential equations with Caputo‐like counterpart hyper‐Bessel operators

Abstract

By studying a weakly singular integral whose kernel involves Mittag‐Leffler functions, we obtain some new Gronwall‐type integral inequalities. Applying these inequalities and fixed point theorems, existence and uniqueness of positive solution of initial value problem to nonlinear fractional differential equation with Caputo‐like counterpart hyper‐Bessel operators are established.