Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Citation - Scopus: 1Fractional Differential Equation With a Complex Potential(Univ Nis, Fac Sci Math, 2020) Ugurlu, Ekin; Tas, Kenan; Baleanu, DumitruIn this manuscript, we discuss the square-integrable property of a fractional differential equation having a complex-valued potential function and we show that at least one of the linearly independent solutions of the fractional differential equation must be squarely integrable with respect to some function containing the imaginary parts of the spectral parameter and the potential function.Article Citation - WoS: 1Citation - Scopus: 1Coordinate-Free Approach for the Characteristic Function of a Fourth-Order Dissipative Operator(Taylor & Francis inc, 2019) Ugurlu, EkinIn this article, we investigate some spectral properties of a singular dissipative fourth-order dissipative operator in case at the singular point. For this purpose we construct the characteristic function of both maximal simple dissipative operator and completely non-unitary contraction which is the Cayley transform of the dissipative operator. Using the properties of the characteristic operator-function we obtain the related results of the boundary value problem. Moreover we obtain the selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing eigenfunctions by using coordinate-free approach.Article Citation - WoS: 3Citation - Scopus: 5Coordinate-Free Approach for the Model Operator Associated With a Third-Order Dissipative Operator(Frontiers Media Sa, 2019) Ugurlu, Ekin; Baleanu, DumitruIn this paper we investigate the spectral properties of a third-order differential operator generated by a formally-symmetric differential expression and maximal dissipative boundary conditions. In fact, using the boundary value space of the minimal operator we introduce maximal selfadjoint and maximal non-selfadjoint (dissipative, accumulative) extensions. Using Solomyak's method on characteristic function of the contractive operator associated with a maximal dissipative operator we obtain some results on the root vectors of the dissipative operator. Finally, we introduce the selfadjoint dilation of the maximal dissipative operator and incoming and outgoing eigenfunctions of the dilation.