Some new Gronwall-Bellman and Bihari type integral inequalities and its applications to Riemann-Liouville fractional differential equations

Source abstract

In this paper, some new variants of Gronwall–Bellman and Bihari type integral inequalities are developed, which generalize some known weakly singular integral inequalities found in the literature. These can be used in the quantitative and qualitative analysis of the solution to certain fractional differential equations. Furthermore, these results are applied to a fractional differential equation to study uniqueness and the dependence of solution on initial conditions and nonlinear terms. The results contribute to the theoretical analysis of fractional differential equations and provide effective tools for studying their qualitative properties. We can also focus on extending these inequalities to other fractional operators and these results can be applied to study the existence, uniqueness, and stability of solutions for more general nonlinear fractional differential equations