Author
Ekin Uğurlu
Other affiliations: Ankara University
Bio: Ekin Uğurlu is an academic researcher from Çankaya University. The author has contributed to research in topics: Dissipative operator & Boundary value problem. The author has an hindex of 10, co-authored 41 publications receiving 534 citations. Previous affiliations of Ekin Uğurlu include Ankara University.
Papers
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TL;DR: In this paper, the authors introduce new fractional integration and differentiation operators based on the standard fractional calculus iteration procedure on conformable derivatives and define spaces and present some theorems related to these operators.
Abstract: This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.
300 citations
TL;DR: In this article, the authors investigated the non-selfadjoint (dissipative) boundary value transmission problem in Weyl's limit-circle case, and showed that all eigenfunctions and associated functions are complete in the space L w 2 ( Ω ).
58 citations
TL;DR: This paper studies the determinant of perturbation connected with the dissipative operator L generated in L^2(I) by (1.1)-(1.5) and investigates the problem of completeness of the system of eigenfunctions and associated functions of L.
45 citations
TL;DR: In this paper, the singular second order differential operators are defined on the multi-interval and some boundary and transmission conditions are imposed on the maximal domain functions with the spectral parameter.
29 citations
TL;DR: In this article, the authors investigated the completeness of the root vectors of a singular dissipative boundary value transmission problem generated by the differential expression l(y) on I, assuming that Weyl's limit-circle case holds for the differential expressions.
Abstract: Let us consider the differential expression
$$\ell (y)=-y^{\prime \prime }+q(x)y,\quad x\in I:=[0,c)\cup (c,\infty ),$$
where c is a transmission point and is regular for the differential expression l(y). We assume that Weyl’s limit-circle case holds for the differential expression l(y) on I. In this paper, using Krein’s theorems, we investigate the completeness of the root vectors of a singular dissipative boundary value transmission problem generated by l(y).
24 citations
Cited by
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01 Jan 2015
3,828 citations
491 citations
TL;DR: Linear Differential Operators By Prof. Cornelius Lanczos as discussed by the authors is a seminal work in the field of linear differential operators, and is a classic example of a linear differential operator.
Abstract: Linear Differential Operators By Prof. Cornelius Lanczos. Pp. xvi + 564. (London: D. Van Nostrand Co., Ltd.; New York: D. Van Nostrand Company, Inc., 1961.) 80s.
366 citations
TL;DR: In this article, a new fractional derivative of the Caputo type is proposed and some basic properties are studied, such as adaptively changing the memory length, the new definition is capable of capturing local memory effect in a distinct way, which is critical in modelling complex systems where the short memory properties has to be considered.
Abstract: In this paper, a new fractional derivative of the Caputo type is proposed and some basic properties are studied. The form of the definition shows that the new derivative is the natural extension of the Caputo one, and that it yields the Caputo derivative with designated memory length. By adaptively changing the memory length, the new definition is capable of capturing local memory effect in a distinct way, which is critical in modelling complex systems where the short memory properties has to be considered. Another attractive property of the new derivative is that it is naturally associated with the Riemann–Liouville definition and as a result, the well established Grunwald–Letnikov approach for numerically solving the fractional differential equation can be readily embedded to approximate the solution of differential equation that involves the new derivatives. Numerical simulations demonstrate the changeable memory effect of the new definition.
160 citations