In this paper, new criteria for a class oscillation of second-order delay differential equations with distributed deviating arguments were established. Our method mainly depends on making sharper estimates for the non-oscillatory solutions of the studied equation. By using the Ricati technique and comparison theorems that compare the studied equations with first-order delay differential equations, we obtained new and less restrictive conditions that ensure the oscillation of all solutions of the studied equation. Further, we give an illustrative example.

In this article, fractional integro-differential inequalities with singular coefficients have been considered. The bounds obtained for investigating the behavior of the solution of a class of singular nonlinear fractional differential equations has been used, some applications are provided.

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