Publication Date:
2021-03-20
Description:
In this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$ egin{aligned}& Delta _{a}^{alpha , eta }y(x)+f_{1} igl(x,y(x+alpha ) igr) =omega (x)+f_{2} igl(x,y(x+ alpha ) igr),quad xin mathbb{N}_{a+n-alpha }, & Delta _{a}^{k-(n-gamma )}y(x) ig|_{x=a+n-gamma } = y_{k}, quad k= 0,1,ldots,n, end{aligned}$$ 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 $lceil alpha
ceil =n$ ⌈ α ⌉ = n , $nin mathbb{N}_{0}$ n ∈ N 0 and $0leq eta leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.
Print ISSN:
1687-1839
Electronic ISSN:
1687-1847
Topics:
Mathematics
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