A Note On Fractional Schrödinger Differential And Difference Equations
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
The initial value problem for the fractional differential equation ? ?? ?? i du dt + Au + Rt 0 ? (s) D1/2 s u (s) ds = f (t) , 0 < t < 1, u (0) = 0 (1) in a Hilbert space H with a self adjoint positive definite operator A is considered. The stability estimates for the solution of this problem and its first derivative under the condition |? (s)| < M1 s 1/2 are established. In practice, the mixed problems for one dimensional fractional Schr¨odinger differential equation with nonlocal boundary conditions in space variable and multidimensional fractional Schr¨odinger differential equation with Dirichlet condition in space variables are considered. The stability estimates for the solution and first order of derivative of the solution of these problems are obtained. The first order of accuracy difference scheme for the approximate solution of this initial value problem is presented. The stability estimate for the solution of this difference scheme and its first order of difference derivative are established. The application of this abstract result to the mixed problems considered above is presented. The stability estimates for the solution and first order of difference derivative of the solution of these difference schemes for these problems are obtained.
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Ashyralyev, A. ve Topçu, B. (2009). A Note On Fractional Schrödinger Differential And Difference Equations. Maltepe Üniversitesi. s. 92.
