Authors:Murat Sari, Huseyin Tunc Pages: 127 - 136 Abstract: In this paper, numerical solutions of the advection-diffusion-reaction (ADR) equation are investigated using the Galerkin, collocation and Taylor-Galerkin cubic B-spline finite element method in strong form of spatial elements using an α-family optimization approach for time variation. The main objective of this article is to capture effective results of the finite element techniques with B-spline basis functions under the consideration of the ADR processes. All produced results are compared with the exact solution and the literature for various versions of problems including pure advection, pure diffusion, advection-diffusion, and advection-diffusion-reaction equations. It is proved that the present methods have good agreement with the exact solution and the literature. PubDate: 2018-02-04 DOI: 10.11121/ijocta.01.2018.00452 Issue No:Vol. 8, No. 2 (2018)

Authors:Erhan Set, Zoubir Dahmani, İlker Mumcu Pages: 137 - 144 Abstract: A number of Chebyshev type inequalities involving various fractional integral operators have, recently, been presented. In this work, motivated essentially by the earlier works and their applications in diverse research subjects, we establish some new Polya-Szego inequality involving generalized Katugampola fractional integral operator and use them to prove some new fractional Chebyshev type inequalities which are extensions of the results in the paper: [On Polya-Szego and Chebyshev type inequalities involving the Riemann-Liouville fractional integral operators, J. Math. Inequal, 10(2) (2016)]. PubDate: 2018-03-09 DOI: 10.11121/ijocta.01.2018.00541 Issue No:Vol. 8, No. 2 (2018)

Authors:Esra Karatas Akgül Pages: 145 - 151 Abstract: On the basis of a reproducing kernel Hilbert space, reproducing kernel functions for solving the coefficient inverse problem for the kinetic equation are given in this paper. Reproducing kernel functions found in the reproducing kernel Hilbert space imply that they can be considered for solving such inverse problems. We obtain approximate solutions by reproducing kernel functions. We show our results by a table. We prove the eciency of the reproducing kernel Hilbert space method for solutions of a coefficient inverse problem for the kinetic equation. PubDate: 2018-04-11 DOI: 10.11121/ijocta.01.2018.00568 Issue No:Vol. 8, No. 2 (2018)

Authors:Youssri H. Youssri, Waleed M. Abd-Elhameed Pages: 152 - 160 Abstract: This paper is dedicated to analyzing and presenting an efficient numerical algorithm for solving a class of fractional optimal control problems (FOCPs). The basic idea behind the suggested algorithm is based on transforming the FOCP under investigation into a coupled system of fractional-order differential equations whose solutions can be expanded in terms of the Jacobi basis. With the aid of the spectral-tau method, the problem can be reduced into a system of algebraic equations which can be solved via any suitable solver. Some illustrative examples and comparisons are presented aiming to demonstrate the accuracy, applicability, and efficiency of the proposed algorithm. PubDate: 2018-04-11 DOI: 10.11121/ijocta.01.2018.00442 Issue No:Vol. 8, No. 2 (2018)

Authors:Yasin Göçgün Pages: 161 - 169 Abstract: We study a dynamic scheduling problem that has the feature of due dates and time windows. This problem arises in chemotherapy scheduling where patients from different types have specific target dates along with time windows for appointment. We consider cancellation of appointments. The problem is modeled as a Markov Decision Process (MDP) and approximately solved using a direct-search based approximate dynamic programming (ADP) tehnique. We compare the performance of the ADP technique against the myopic policy under diverse scenarios. Our computational results reveal that the ADP technique outperforms the myopic policy on majority of problem sets we generated. PubDate: 2018-04-22 DOI: 10.11121/ijocta.01.2018.00469 Issue No:Vol. 8, No. 2 (2018)

Authors:Özal Yildirim, Ulas Baran Baloglu Pages: 170 - 175 Abstract: In this study, a feature vector optimization based method has been proposed for classification of the heartbeat types. Electrocardiogram (ECG) signals of five different heartbeat type were used for this aim. Firstly, wavelet transform (WT) method were applied on these ECG signals to generate all feature vectors. Optimizing these feature vectors is provided by performing particle swarm optimization (PSO), genetic search, best first, greedy stepwise and multi objective evoluationary algorithms on these vectors. These optimized feature vectors are later applied to the classifier inputs for performance evaluation. A comprehensive assessment was presented for the determination of optimized feature vectors for ECG signals and best-performing classifier for these optimized feature vectors was determined. PubDate: 2018-04-12 DOI: 10.11121/ijocta.01.2018.00567 Issue No:Vol. 8, No. 2 (2018)

Authors:Fuat Usta Pages: 176 - 182 Abstract: In this paper we introduced the conformable derivatives and integrals of radial basis functions (RBF) to solve conformable fractional differential equations via RBF collocation method. For that, firstly, we found the conformable derivatives and integrals of power, Gaussian and multiquadric basis functions utilizing the rule of conformable fractional calculus. Then by using these derivatives and integrals we provide a numerical scheme to solve conformable fractional differential equations. Finally we presents some numerical results to confirmed our method PubDate: 2018-04-22 DOI: 10.11121/ijocta.01.2018.00544 Issue No:Vol. 8, No. 2 (2018)

Authors:O. Tolga Altinoz Pages: 183 - 194 Abstract: In this study, the PID tuning method (controller design scheme) is proposed for a linear quarter model of active suspension system installed on the vehicles. The PID tuning scheme is considered as a multiobjective problem which is solved by converting this multiobjective problem into single objective problem with the aid of scalarization approaches. In the study, three different scalarization approaches are used and compared to each other. These approaches are called linear scalarization (weighted sum), epsilon-constraint and Benson’s methods. The objectives of multiobjective optimization are selected from the time-domain properties of the transient response of the system which are overshoot, rise time, peak time and error (in total there are four objectives). The aim of each objective is to minimize the corresponding property of the time response of the system. First, these four objective is applied to the scalarization functions and then single objective problem is obtained. Finally, these single objective problems are solved with the aid of heuristic optimization algorithms. For this purpose, four optimization algorithms are selected, which are called Particle Swarm Optimization, Differential Evolution, Firefly, and Cultural Algorithms. In total,twelve implementations are evaluated with the same number of iterations. In this study, the aim is to compare the scalarization approaches and optimization algorithm on active suspension control problem. The performance of the corresponding cases (implementations) are numerically and graphically demonstrated on transient responses of the system. PubDate: 2018-04-22 DOI: 10.11121/ijocta.01.2018.00399 Issue No:Vol. 8, No. 2 (2018)

Authors:Hasan Dalman Pages: 195 - 200 Abstract: In many situations, uncertainty and randomness concurrently occur in a system. Thus this paper presents a new concept for uncertain random variable. Also, a simulation algorithm based on uncertain random variables is presented to approximate the chance distribution using pessimistic value and optimistic value. An example is also given to illustrate how to use the presented simulation algorithm. PubDate: 2018-04-25 DOI: 10.11121/ijocta.01.2018.00601 Issue No:Vol. 8, No. 2 (2018)

Authors:Yusuf Altun Pages: 201 - 207 Abstract: This paper proposes a gain scheduling linear quadratic integral (LQI) servo controller design, which is derived from linear quadratic regulator (LQR) optimal control, for non-singular linear parameter varying (LPV) descriptor systems. It is assumed that state space matrices are non-singular since many mechanical systems do not have any non-singular matrices such as the natural state space forms of robotic manipulator, pendulum and suspension systems. A controller design is difficult for the systems due to rational LPV case. Therefore, the proposed gain scheduling controller is designed without the difficulty. Accordingly, the motion control design is implemented for two-link flexible joint robotic manipulator. Finally, the control system simulation is performed to prove the applicability and performance. PubDate: 2018-04-27 DOI: 10.11121/ijocta.01.2018.00564 Issue No:Vol. 8, No. 2 (2018)

Authors:Nuşin Uncu, Berna Bulğurcu, Fatih Kılıç Pages: 208 - 215 Abstract: Pharmacies are considered as an integral part of health care systems for supplying medicine to patients. In order to access medicine with ease, pharmacies locations in the context of distance and demand are important for patients. In the case of a few numbers of pharmacies may be on duty at nights or during holidays, pharmacies duty scheduling problem occur and can be associated with location models. In contrast to widely used p-median model which aims to minimize the demand-weighted distance, we maximize the demand covered over the distance between the patients and the pharmacies on duty. Main contribution of the proposed model is the restriction constraint for the distance between pharmacies on duty in order to ensure fairness in an organizational view of point. We propose a distance restricted maximal covering location model (DR-MCLM) in this study. This mathematical model is a mixed integer linear programming model and solved by Lingo optimization software. The distances between the pharmacies and the sites are obtained using Geographic Information Systems (GIS). The model is applied for the case in Adana, one of the biggest cities in Turkey. The results are given on the maps of the city, including the pharmacies on duty and their assignments to sites in each day of the period. PubDate: 2018-06-01 DOI: 10.11121/ijocta.01.2018.00557 Issue No:Vol. 8, No. 2 (2018)

Authors:Nurhan Gursel Ozmen, Levent Gumusel Pages: 216 - 227 Abstract: In brain computer interface (BCI) research, electroencephalography (EEG) is the most widely used method due to its noninvasiveness, high temporal resolution and portability. Most of the EEG-based BCI studies are aimed at developing methodologies for signal processing, feature extraction and classification. In this study, an experimental EEG study was carried out with six subjects performing imagery mental and motor tasks. We present a multi-class EEG decoding with a novel pairwise output coding method of EEGs to improve the performance of self-induced BCI systems. This method involves an augmented one-versus-one multiclass classification with less time and reduced number of electrodes. Furthermore, a train repetition number is introduced in the training step to optimize the data selection. The difference among right and left hemispheres is also searched. Finally, the difference between experienced and novice subjects is also observed. The experimental results have demonstrated that, the use of proposed classification algorithm produces high classification accuracies (98%) with nine channels. Reduced numbers of channels (four channels) have 100% accuracies for mental tasks and 87% accuracies for motor tasks with Support Vector Machines (SVM). The classification accuracies are quite high though the proposed one-versus-one technique worked well compared to the classical method. The results would be promising for a real-time study. PubDate: 2018-07-15 DOI: 10.11121/ijocta.01.2018.00516 Issue No:Vol. 8, No. 2 (2018)

Authors:Nilay Akgonullu Pirim, Fatma Ayaz Pages: 228 - 236 Abstract: This paper focuses on the approximate solutions of the higher order fractional differential equations with multi terms by the help of Hermite Collocation method (HCM). This new method is an adaptation of Taylor's collocation method in terms of truncated Hermite Series. With this method, the differential equation is transformed into an algebraic equation and the unknowns of the equation are the coefficients of the Hermite series solution of the problem. This method appears as a useful tool for solving fractional differential equations with variable coefficients. To show the pertinent feature of the proposed method, we test the accuracy of the method with some illustrative examples and check the error bounds for numerical calculations. PubDate: 2018-07-20 DOI: 10.11121/ijocta.01.2018.00610 Issue No:Vol. 8, No. 2 (2018)

Authors:Halil Ibrahim Basturk Pages: 237 - 249 Abstract: We design adaptive algorithms for both cancellation and estimation of unknown periodic disturbance, by feedback of state--derivatives ( i.e.,} without position information for mechanical systems) for the plants which are modeled as a linear time invariant system. We consider a series of unmatched unknown sinusoidal signals as the disturbance. The first step of the design consists of the parametrization of the disturbance model and the development of observer filters. The result obtained in this step allows us to use adaptive control techniques for the solution of the problem. In order to handle the unmatched condition, a backstepping technique is employed. Since the partial measurement of the virtual inputs is not available, we design a state observer and the estimates of these signals are used in the backstepping design. Finally, the stability of the equilibrium of the adaptive closed loop system with the convergence of states is proven. As a numerical example, a two-degree of freedom system is considered and the effectiveness of the algorithms are shown. PubDate: 2018-07-20 DOI: 10.11121/ijocta.01.2018.00519 Issue No:Vol. 8, No. 2 (2018)

Authors:Aydin Secer Pages: 250 - 258 Abstract: In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically. PubDate: 2018-07-24 DOI: 10.11121/ijocta.01.2018.00608 Issue No:Vol. 8, No. 2 (2018)

Authors:İmdat İşcan, Mahir Kadakal, Alper Aydın Pages: 259 - 265 Abstract: This paper is about obtaining some new type of integral inequalities for functions from the Lipschitz class. For this, some new integral inequalities related to the differences between the two different types of integral averages for Lipschitzian functions are obtained. Moreover, applications for some special means as arithmetic, geometric, logarithmic, -logarithmic, harmonic, identric are given. PubDate: 2018-07-24 DOI: 10.11121/ijocta.01.2018.00565 Issue No:Vol. 8, No. 2 (2018)

Authors:Reyhan Irkin, Nihal Yilmaz Ozgur, Nihal Tas Pages: 266 - 275 Abstract: Lactic acid fermented vegetables are important sources of vitamins and minerals. In recent years consumers demand for non-dairy based functional products has increased. Cabbage pickle has high enough concentrations of fiber and also it may show health effect with the containing high numbers of lactic acid bacteria. The aim of this study is to optimize mathematically cabbage-carrot pickle fermentation for the viability of Lactobacillus acidophilus, Lactobacillus casei cultures and the sensory scores in brine with 5% and 7% (w/v) salt concentrations. Viability optimization of lactic acid bacteria is done via the notion of “fuzzy soft set” method. Lb. casei, Lb. acidophilus, total lactic acid bacteria, Enterobacteriaceae sp., yeast-mould counts and pH values have been reported during the 30 days of storage. The results are compared with the control traditional fermented cabbage-carrot pickle. Organoleptic properties are evaluated. We conclude that the fermented pickle samples contain a significant number of beneficial lactic acid bacteria and high sensory marks at the end of the storage. PubDate: 2018-07-31 DOI: 10.11121/ijocta.01.2018.00457 Issue No:Vol. 8, No. 2 (2018)

Authors:Çağrı Koç, Mehmet Erbaş, Eren Ozceylan Pages: 276 - 287 Abstract: This paper introduces, models, and solves a rich vehicle routing problem (VRP) motivated by the case study of replenishment of automated teller machines (ATMs) in Turkey. In this practical problem, commodities can be taken from the depot, as well as from the branches to efficiently manage the inventory shortages at ATMs. This rich VRP variant concerns with the joint multiple depots, pickup and delivery, multi-trip, and homogeneous fixed vehicle fleet. We first mathematically formulate the problem as a mixed-integer linear programming model. We then apply a Geographic Information System (GIS)-based solution method, which uses a tabu search heuristic optimization method, to a real dataset of one of the major bank. Our numerical results show that we are able to obtain solutions within reasonable solution time for this new and challenging practical problem. The paper presents computational and managerial results by analyzing the trade-offs between various constraints. PubDate: 2018-07-31 DOI: 10.11121/ijocta.01.2018.00572 Issue No:Vol. 8, No. 2 (2018)