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Citation - WoS: 52
Citation - Scopus: 63
A Numerical Schemes and Comparisons for Fixed Point Results With Applications To the Solutions of Volterra Integral Equations in Dislocated Extended B - Metric Space
(Elsevier, 2020) Karapinar, Erdal; Atangana, Abdon; Panda, Sumati Kumari
In this article, we propose a generalization of both b-metric and dislocated metric, namely, dislocated extended b-metric space. After getting some fixed point results, we suggest a relatively simple solution for a Volterra integral equation by using the technique of fixed point in the setting of dislocated extended b-metric space. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Citation - WoS: 2
Citation - Scopus: 4
A New Systematic and Flexible Method for Developing Hierarchical Decision-Making Models
(Tubitak Scientific & Technological Research Council Turkey, 2015) Beldek, Ulas; Leblebicioglu, Mehmet Kemal
The common practice in multilevel decision-making (DM) systems is to achieve the final decision by going through a finite number of DM levels. In this study, a new multilevel DM model is proposed. This model is called the hierarchical DM (HDM) model and it is supposed to provide a flexible way of interaction and information flow between the consecutive levels that allows policy changes in DM procedures if necessary. In the model, in the early levels, there are primary agents that perform DM tasks. As the levels increase, the information associated with these agents is combined through suitable processes and agents with higher complexity are formed to carry out the DM tasks more elegantly. The HDM model is applied to the case study 'Fault degree classification in a 4-tank water circulation system'. For this case study, the processes that connect the lower levels to the higher levels are agent development processes where a special decision fusion technique is its integral part. This decision fusion technique combines the previous level's decisions and their performance indicator suitably to contribute to the improvement of new agents in higher levels. Additionally, the proposed agent development process provides flexibility both in the training and validation phases, and less computational effort is required in the training phase compared to a single-agent development simulation carried out for the same DM task under similar circumstances. Hence, the HDM model puts forward an enhanced performance compared to a single agent with a more sophisticated structure. Finally, model validation and efficiency in the presence of noise are also simulated. The adaptability of the agent development process due to the flexible structure of the model also accounts for improved performance, as seen in the results.
Citation - WoS: 131
Citation - Scopus: 148
On an Accurate Discretization of a Variable-Order Fractional Reaction-Diffusion Equation
(Elsevier Science Bv, 2019) Jajarmi, Amin; Baleanu, Dumitru; Sun, HongGuang; Hajipour, Mojtaba
The aim of this paper is to develop an accurate discretization technique to solve a class of variable-order fractional (VOF) reaction-diffusion problems. In the spatial direction, the problem is first discretized by using a compact finite difference operator. Then, a weighted-shifted Grunwald formula is applied for the temporal discretization of fractional derivatives. To solve the derived nonlinear discrete system, an accurate iterative algorithm is also formulated. The solvability, stability and L-2-convergence of the proposed scheme are derived for all variable-order alpha(t) is an element of (0, 1). The proposed method is of accuracy-order O(tau(3) + h(4)), where tau and h are temporal and spatial step sizes, respectively. Through some numerical simulations, the theoretical analysis and high-accuracy of the proposed method are verified. Comparative results also indicate that the accuracy of the new discretization technique is superior to the other methods available in the literature. Finally, the feasibility of the proposed VOF model is demonstrated by using the reported experimental data. (C) 2018 Elsevier B.V. All rights reserved.
A New Algorithm To Locate the Zero Fields in Antenna Radiation Pattern Measurements
(Taylor & Francis Ltd, 2013) Sener, G.
This article describes a new method to determine the directions of the zero fields in antenna radiation measurements. Zero-field detection is important when there are null constraints in antenna analysis or synthesis. To identify the directions of the zero fields, the general practice is to measure the propagating field in a number of small incremental angles in 2D space. For an antenna with narrow beam characteristics, even more sampling is necessary for accuracy. As a result, the time efficiency is decreased. In order to speed up the process, an optimization algorithm may be employed such that the measurements may converge to the zero-field locations faster. However, the difficulty is that many optimization algorithms require the use of derivatives of the pattern function. The algorithm proposed in this paper is derivative free and utilizes only the amplitude data, hence it is suitable and applicable to antenna measurements providing time efficiency.
Citation - WoS: 12
Citation - Scopus: 16
An Avant-Garde Handling of Temporal-Spatial Fractional Physical Models
(Walter de Gruyter Gmbh, 2020) Alquran, Marwan; Katatbeh, Qutaibeh; Yousef, Feras; Momani, Shaher; Baleanu, Dumitru; Jaradat, Imad
In the present study, we dilate the differential transform scheme to develop a reliable scheme for studying analytically the mutual impact of temporal and spatial fractional derivatives in Caputo's sense. We also provide a mathematical framework for the transformed equations of some fundamental functional forms in fractal 2-dimensional space. To demonstrate the effectiveness of our proposed scheme, we first provide an elegant scheme to estimate the (mixed-higher) Caputo-fractional derivatives, and then we give an analytical treatment for several (non)linear physical case studies in fractal 2-dimensional space. The study concluded that the proposed scheme is very efficacious and convenient in extracting solutions for wide physical applications endowed with two different memory parameters as well as in approximating fractional derivatives.