Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article A Class of Time-Fractional Dirac Type Operators(Pergamon-Elsevier Science Ltd, 2021) Baleanu, Dumitru; Restrepo, Joel E.; Suragan, DurvudkhanBy using a Witt basis, a new class of time-fractional Dirac type operators with time-variable coefficients is introduced. These operators lead to considering a wide range of fractional Cauchy problems. Solutions of the considered general fractional Cauchy problems are given explicitly. The representations of the solutions can be used efficiently for analytic and computational purposes. We apply the obtained representation of a solution to recover a variable coefficient solution of an inverse fractional Cauchy problem. Some concrete examples are given to show the diversity of the obtained results. (c) 2020 Elsevier Ltd. All rights reserved.Correction Corrigendum To “Numerical Investigation of Magneto-Thermal Impact on Phase Change Phenomenon of Nano-PCM Within a Hexagonal Shaped Thermal Energy Storage” [Appl. Thermal Eng., (2023) 223, 119984](s1359431123000133)(10.1016/J.applthermaleng.2023.119984)(Pergamon-Elsevier Science Ltd, 2025) Izadi, Mohsen; Sheremet, Mikhail; Hajjar, Ahmad; Galal, Ahmed M.; Mahariq, Ibrahim; Jarad, Fahd; Hamida, Mohamed Bechir Ben; Ben Hamida, Mohamed BechirArticle Citation - WoS: 1Citation - Scopus: 1Left-Definite Fractional Hamiltonian Systems: Titchmarsh-Weyl Theory(Pergamon-Elsevier Science Ltd, 2025) Ugurlu, EkinHamiltonian systems are useful when formally symmetric boundary value problems generated by ordinary derivatives are considered. However, if the ordinary derivatives are changed by non-integer-order (fractional) derivatives, it is not easy to investigate the corresponding problems. In this paper, we introduce a systematic approach to dealing with fractional boundary value problems by constructing a fractional Hamiltonian system. In particular, we consider a left-definite system, and we construct nested-circles theory (Weyl theory) for this system of equations. Using the Titchmarsh-Weyl function, we prove that at least r-solutions of the 2r-dimensional system of equations should be Dirichlet-integrable on a given interval.Article Citation - WoS: 1Citation - Scopus: 1The Neural Correlates of Cognitive Load in Learning: an Fmri Study on Graph Comprehension(Pergamon-Elsevier Science Ltd, 2025) Ozcelik, ErolBackground: Cognitive load theory suggests that excessive demands on the human cognitive system can lead to cognitive overload and impaired learning. However, whilst the neural correlates of cognitive load are unclear, neuroimaging techniques such as functional magnetic resonance imaging (fMRI) may help provide answers to these questions. Aims: Considering this potential, this study aims to investigate which brain structures are associated with cognitive load through conducting an fMRI study on graph comprehension. Sample: The study's sample consists of 15 undergraduate students. Methods: Based on a within-subjects design, participants answered comprehension questions using split (i.e., high cognitive load) and integrated (i.e., low cognitive load) graphs whilst undergoing a magnetic resonance imaging (MRI) scan. Results: Participants exhibited lower levels of accuracy and slower reaction times with split graphs compared to integrated graphs. The fMRI data showed that cognitive load was associated with the frontoparietal network. More specifically, the multiple demand network revealed greater activation in graphs with higher cognitive load than those of lower cognitive load. Conclusions: These findings may indicate that a domain-general attentional brain network is responsible for cognitive load.Article Citation - WoS: 18Citation - Scopus: 22A Class of Time-Fractional Dirac Type Operators(Pergamon-Elsevier Science Ltd, 2021) Baleanu, Dumitru; Restrepo, Joel E.; Suragan, DurvudkhanBy using a Witt basis, a new class of time-fractional Dirac type operators with time-variable coefficients is introduced. These operators lead to considering a wide range of fractional Cauchy problems. Solutions of the considered general fractional Cauchy problems are given explicitly. The representations of the solutions can be used efficiently for analytic and computational purposes. We apply the obtained representation of a solution to recover a variable coefficient solution of an inverse fractional Cauchy problem. Some concrete examples are given to show the diversity of the obtained results. (c) 2020 Elsevier Ltd. All rights reserved.Article Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations(Pergamon-Elsevier Science Ltd, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; Bleanu, DumitruWe establish the long-time asymptotic formula of solutions to the (1+α)-order fractional differential equation 0iOt1+αx+a(t)x=0, t>0, under some simple restrictions on the functional coefficient a(t), where 0iOt1+α is one of the fractional differential operators 0Dtα(x′), (0Dtαx)′= 0Dt1+αx and 0Dtα(tx′-x). Here, 0Dtα designates the Riemann-Liouville derivative of order α∈(0,1). The asymptotic formula reads as [b+O(1)] ·xsmall+c·xlarge as t→+∞ for given b, c∈R, where xsmall and xlarge represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation 0iOt1+αx=0, t>0