In this manuscript, we studied stability of fractional order delayed differential equations with two fractional terms and gave some criteria on the stability of equation (1.1) - (1.2). The type of equation that we have considered in this article is the type of equation that has more general and more complex application areas than the equations discussed so far, and the examination of such an equation type colud not been seen in the literature until now. We use some well known inequalities for the proof of our results. We also provide some examples to check the accuracy of our results.

In this manuscript new oscillation criteria are given for solutions of h-order delay difference equation in the form ∆ E n + p n E n − α = 0 . Here, four cases of p are considered; for α∈N , as oscillatory periodic sequences with periods 2 α,(2 α+1) and ( α+1) , and a quickly oscillating sequence such that p n p n + 1 < 0 . It is well known that coefficient functions has a very important role in the behavior of the solutions of an equation. The coefficients sequence p has been considered as positive sequences in all oscillation criteria so far. But It is considered as a oscillatory periodic sequences and quickly oscillatory sequences for the first time in this study. We use a new technique to prove our results. Also some examples are provided to demonstrate the effectiveness of the main results.