Tuğba YALÇIN UZUN, Sermin ÖZTÜRK, Hüsniye ÖZ

Sönüm Terimli Caputo Kesirli Fark Denklemlerinin Salınımlılığı

Bu makalede, ? ∈ (? − 1, ?) bir sabit (? ∈ ℕ) ∆???, ?’in ?-yıncı mertebeden kesirli Caputo kesirli farkoperatörü ve ℕ0 = {0,1,2,… } olmak üzere, ∆??(?)|?=0 = ??,? = 1,2,…, ? − 1 başlangıç şartına sahip(1 + ?(?))∆(∆???(?)) + ?(?)∆???(?) + ?(?, ?(?)) = ?(?), ? ∈ ℕ0ile verilen ikinci taraflı sönüm terimlikesirli fark denkleminin salınımlılığı için bir yeter şart elde edilmiştir. Bu çalışma için “?(?) ve ?(?) reelfonksiyonlar, ?(?) > −1, ?: ℕ0 × ℝ ⟶ ℝ ve ? ≠ 0, ?0 ∈ ℕ0” önermesi geçerlidir. Makalenin sonundaaçıklayıcı bir örnek verilmiştir.

Oscillation of Caputo Fractional Difference Equations with Damping Term

In this paper, we obtain a sufficent condition for the oscillation of forced fractional difference equations with damping term of the form (1 + ?(?))∆(∆? ??(?)) + ?(?)∆? ??(?) + ?(?, ?(?)) = ?(?), ? ∈ ℕ0with initial condition ∆ ??(?)|?=0 = ??, ? = 1,2,… , ? − 1 where ? ∈ (? − 1, ?) is a constant (? ∈ ℕ), ∆? ?? is the Caputo fractional difference operator of order ? of ? and ℕ0 = {0,1,2,… }. For this study, the proposition “?(?) and ?(?) are real functions, ?(?) > −1, ?: ℕ0 × ℝ ⟶ ℝ and ? ≠ 0, ?0 ∈ ℕ0 ” is held. An illustrative example is given at the end of the paper.

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