A Note On Fractional Schrödinger Differential And Difference Equations
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CitationAshyralyev, A. ve Topçu, B. (2009). A Note On Fractional Schrödinger Differential And Difference Equations. Maltepe Üniversitesi. s. 92.
The initial value problem for the fractional differential equation i du dt + Au + Rt 0 α (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 |α (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.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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