In this paper, we establish some new weakly singular Volterra type integral inequalities that include the maxima of the unknown function of two variables. We also use the results to research the boundedness of solutions to retarded nonlinear Volterra type integral equations.

This paper established some new Hermite–Hadamard type inequalities for ψ-Riemann–Liouville fractional integrals via convex functions. As applications, we applied the inequalities to special means of real numbers and constructed inequalities for the beta function.

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