Compact Finite Differences Method And Caputo Fractional Derivative Definition For Lineer Fractional Schrödingerequations
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In this paper, linear fractional Schrödinger equation is studied by using compact finite differences method. The fractional part of the equation is worked by applying Caputo fractional derivative definition. In the solution of the problem, finite differences discretization along the time, and fifth-order compact finite differences scheme along the spatial coordinate have been applied. Dispersion analysis is applied to ensure consistency and convergency of the method used. The result shows that the applied method in this study is an applicable technique and approximates the exact solution very well.
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Çağlar, Mert; Polatoğlu, Yaşar; Yavuz, Emel (2008)For analytic function f(z) = z + a2z 2 + · · · in the open unit disc D, a new fractional operator Dλf(z) is defined. Applying this fractional operator Dλf(z) and the principle of subordination, we give new proofs for ...
Polatoğlu, Yaşar; Yavuz, Emel (International Symposium on Geometric Function Theory and Applications, 2007, Istanbul Kültür University, Istanbul, Turkey, 2007)
Polatoğlu, Yaşar; Yavuz, Emel; Owa, Shigeyoshi; Nakamura, Yayoi (2008)Let A be the class of analytic functions f(z) in the open unit disc U with f(0) = 0 and f (0) = 1. Applying the fractional calculus for f(z) ∈ A, the fractional operator Dλf(z) is defined. Further, a new subclass S∗ λ ...