https://hdl.handle.net/20.500.12809/238 Sun, 19 Apr 2026 13:41:43 GMT 2026-04-19T13:41:43Z https://hdl.handle.net/20.500.12809/10928 Basic theory of s-posets Kandemir, Mustafa Burç In this paper, we have established the notions of soft order relations and studied its basic structural properties. We give the concepts of soft maximum, soft minimum, soft maximal, soft minimal, soft infimum and soft supremum in any s-poset. Then, the concept of soft order preserving mapping is defined and given some basic results. Moreover, it has been shown that the topology derived from a soft partial order relation is a soft topology which will substitute as a soft version of Alexandroff topology in classical theory. With all that, we obtained the category SPOSET of s-posets, and constructed a functor which is called ostracizer functor between the categories SPOSET and POSET . Sun, 01 Jan 2023 00:00:00 GMT https://hdl.handle.net/20.500.12809/10928 2023-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/10859 Towards solving linear fractional differential equations with Hermite operational matrix Koşunalp, Hatice Yalman; Gülsu, Mustafa This paper presents the derivation of a new operational matrix of Caputo fractional derivatives through Hermite polynomials with Tau method to solve a set of fractional differential equations (FDEs). The proposed algorithm is intended to solve linear type of FDEs with the pre-defined conditions into a matrix form for redefining the complete problem as a system of a algebraic equations.The proposed strategy is then applied to solve the simplified FDEs in linear form. To assess the performance of the proposed method, exact and approximate solutions for a number of illustrative examples are obtained which prove the effectiveness of the idea. Sun, 01 Jan 2023 00:00:00 GMT https://hdl.handle.net/20.500.12809/10859 2023-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/10846 A Numerical Scheme for Time-Fractional Fourth-Order Reaction-Diffusion Model Koç, Dilara Altan In fractional calculus, the fractional differential equation is physically and theoretically important. In this article an efficient numerical process has been developed. Numerical solutions of the time fractional fourth order reaction diffusion equation in the sense of Caputo derivative is obtained by using the implicit method, which is a finite difference method and is developed by increasing the number of iterations. The advantage of the implicit difference scheme is unconditionally stable. The stability analysis and convergency have been proven. A numerical example has been presented, and the validity of the method is supported by tables and graphics. Sun, 01 Jan 2023 00:00:00 GMT https://hdl.handle.net/20.500.12809/10846 2023-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/10762 Novel Graph Neighborhoods Emerging from Ideals Çaksu Güler, Ayşegül; Balcı, Mehmet Ali; Batrancea, Larissa M.; Akgüller, Ömer; Gaban, Lucian Rough set theory is a mathematical approach that deals with the problems of uncertainty and ambiguity in knowledge. Neighborhood systems are the most effective instruments for researching rough set theory in general. Investigations on boundary regions and accuracy measures primarily rely on two approximations, namely lower and upper approximations, by using these systems. The concept of the ideal, which is one of the most successful and effective mathematical tools, is used to obtain a better accuracy measure and to decrease the boundary region. Recently, a generalization of Pawlak’s rough set concept has been represented by neighborhood systems of graphs based on rough sets. In this research article, we propose a new method by using the concepts of the ideal and different neighborhoods from graph vertices. We examine important aspects of these techniques and produce accuracy measures that exceed those previously = reported in the literature. Finally, we show that our method yields better results than previous techniques utilized in chemistry. Sun, 01 Jan 2023 00:00:00 GMT https://hdl.handle.net/20.500.12809/10762 2023-01-01T00:00:00Z