Narrow Results

The aim of this paper is to generalize some integral inequalities of Gronwall–Bellman type. We generalize the results presented by Pachpatte in [Inequalities for Differential and Integral Equations (Academic Press, New York, 1998)] and Abdeldaim in [On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation, J. Egypt. Math. Sci. Lett.23 (2015) 470–475] and also establish some new forms.

In this paper, a class of nonlinear weakly singular integral inequality is investigated, which includes a non-constant term outside the integrals. The upper bounds of the embedded unknown functions are estimated explicitly by adopting novel analysis techniques, such as: the definitions and rules of conformable fractional differential and conformable fractional integration, the techniques of change of variable, and the method of amplification. The derived results can be applied in the study of qualitative properties of solutions of conformable fractional integral equations.