This paper deals with obtaining some sufficient conditions for oscillation of high order neutral fractional integro-differential equations. The obtained results are mentioned for the first time in the literature for the oscillation of Caputo-Fabrizio fractional integro-differential equations. Finally, an illustrative example is given to verify our main results.

This paper deals with obtaining some sufficient conditions for oscillation of high order neutral fractional integro-differential equations. The obtained results are mentioned for the first time in the literature for the oscillation of Caputo-Fabrizio fractional integro-differential equations. Finally, an illustrative example is given to verify our main results.

In this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$\begin{aligned}& \Delta _{a}^{\alpha ,\beta }y(x)+f_{1} \bigl(x,y(x+\alpha ) \bigr) =\omega (x)+f_{2} \bigl(x,y(x+ \alpha ) \bigr),\quad x\in \mathbb{N}_{a+n-\alpha }, \\& \Delta _{a}^{k-(n-\gamma )}y(x) \big|_{x=a+n-\gamma } = y_{k}, \quad k= 0,1,\ldots,n, \end{aligned}$$ Δ a α , β y ( x ) + f 1 ( x , y ( x + α ) ) = ω ( x ) + f 2 ( x , y ( x + α ) ) , x ∈ N a + n − α , Δ a k − ( n − γ ) y ( x ) | x = a + n − γ = y k , k = 0 , 1 , … , n , where $\lceil \alpha \rceil =n$ ⌈ α ⌉ = n , $n\in \mathbb{N}_{0}$ n ∈ N 0 and $0\leq \beta \leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.

Salınımlılık; İkinci taraflı kesirli fark denklemi; Sönüm terimi; Caputo fark operatörü Öz Bu makalede, ∈ ( − 1, ) bir sabit ( ∈ ℕ) ∆ , 'in -yıncı mertebeden kesirli Caputo kesirli fark operatörü ve ℕ 0 = {0,1,2, … } olmak üzere, ∆ ( )| =0 = , = 1,2, … , − 1 başlangıç şartına sahip (1 + ( ))∆(∆ ( )) + ( )∆ ( ) + ( , ( )) = ( ), ∈ ℕ 0 ile verilen ikinci taraflı sönüm terimli kesirli fark denkleminin salınımlılığı için bir yeter şart elde edilmiştir. Bu çalışma için " ( ) ve ( ) reel fonksiyonlar, ( ) > −1, : ℕ 0 × ℝ ⟶ ℝ ve ≠ 0, 0 ∈ ℕ 0 " önermesi geçerlidir. Makalenin sonunda açıklayıcı bir örnek verilmiştir.

In this paper, we study the forced oscillatory theory for higher order fractional differential equations with damping term via Ψ-Hilfer fractional derivative. We get sufficient conditions which ensure the oscillation of all solutions and give an illustrative example for our results. The Ψ-Hilfer fractional derivative according to the choice of the Ψ function is a generalization of the different fractional derivatives defined earlier. The results obtained in this paper are a generalization of the known results in the literature, and present new results for some fractional derivatives.