Existence, uniqueness, estimation and continuous dependence of the solutions of a nonlinear integral and an integrodifferential equations of fractional order

By means of two fractional order integral inequalities we investigate the existence and uniqueness of the solutions of the fractional nonlinear Volterra integral equation and a fractional nonlinear integrodifferential equation in Banach space $C_{\xi}$, using an adequate norm, $||\cdot||_{\xi,\infty}$. We estimate the solutions and investigate their continuous dependence.