WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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A 3D virtual environment for training soccer referees
(Elsevier Science Bv, 2019) Güleç, Ulaş; Gulec, Ulas; Yilmaz, Murat; Yılmaz, Murat; Isler, Veysi; O'Connor, Rory V.; Clarke, Paul M.; 47439
Emerging digital technologies are being used in many ways by and in particular virtual environments provide new opportunities to gain experience on real-world phenomena without having to live the actual real-world experiences. In this study, a quantitative research approach supported by expert validation interviews was conducted to determine the availability of virtual environments in the training of soccer referees. The aim is to design a virtual environment for training purposes, representing a real-life soccer stadium to allow the referees to manage matches in an atmosphere similar to the real stadium atmosphere. At this point, the referees have a chance to reduce the number of errors that they make in real life by experiencing difficult decisions that they encounter during the actual match via using the virtual stadium. In addition, the decisions and reactions of the referees during the virtual match were observed with the number of different fans in the virtual stadium to understand whether the virtual stadium created a real stadium atmosphere for the referees. For this evaluation, Presence Questionnaire (PQ) and Immersive Tendencies Questionnaire (ITQ) were applied to the referees to measure their involvement levels. In addition, a semi-structure interview technique was utilized in order to understand participants' opinions about the system. These interviews show that the referees have a positive attitude towards the system since they can experience the events occurred in the match as a first person instead of watching them from camera as a third person. The findings of current study suggest that virtual environments can be used as a training tool to increase the experience levels of the soccer referees since they have an opportunity to decide about the positions without facing the real-world risks.
A Gronwall inequality via the generalized proportional fractional derivative with applications
(Springer, 2019) Alzabut, Jehad; Alzabut, Jehad; Abdeljawad, Thabet; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Sudsutad, Weerawat; 234808
In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its features. As an application, we accommodate the newly defined derivative to prove the uniqueness and obtain a bound in terms of Mittag-Leffler function for the solutions of a nonlinear delay proportional fractional system. An example is presented to demonstrate the applicability of the theory.
A linearization-based approach of homotopy analysis method for non-linear time-fractional parabolic PDEs
(Wiley, 2019) Odibat, Zaid; Baleanu, Dumitru; Baleanu, Dumitru; 56389
In this paper, a novel approach, namely, the linearization-based approach of homotopy analysis method, to analytically treat non-linear time-fractional PDEs is proposed. The presented approach suggests a new optimized structure of the homotopy series solution based on a linear approximation of the non-linear problem. A comparative study between the proposed approach and standard homotopy analysis approach is illustrated by solving two examples involving non-linear time-fractional parabolic PDEs. The performed numerical simulations demonstrate that the linearization-based approach reduces the computational complexity and improves the performance of the homotopy analysis method.
A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets
(Mdpi, 2019) Baleanu, Dumitru; Baleanu, Dumitru; Jassim, Hassan Kamil; 56389
In this paper, we apply a new technique, namely, the local fractional Laplace homotopy perturbation method (LFLHPM), on Helmholtz and coupled Helmholtz equations to obtain analytical approximate solutions. The iteration procedure is based on local fractional derivative operators (LFDOs). This method is a combination of the local fractional Laplace transform (LFLT) and the homotopy perturbation method (HPM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence
(Amer inst Physics, 2019) Jajarmi, Amin; Baleanu, Dumitru; Ghanbari, Behzad; Baleanu, Dumitru; 56389
The main objective of this research is to investigate a new fractional mathematical model involving a nonsingular derivative operator to discuss the clinical implications of diabetes and tuberculosis coexistence. The new model involves two distinct populations, diabetics and nondiabetics, while each of them consists of seven tuberculosis states: susceptible, fast and slow latent, actively tuberculosis infection, recovered, fast latent after reinfection, and drug-resistant. The fractional operator is also considered a recently introduced one with Mittag-Leffler nonsingular kernel. The basic properties of the new model including non-negative and bounded solution, invariant region, and equilibrium points are discussed thoroughly. To solve and simulate the proposed model, a new and efficient numerical method is established based on the product-integration rule. Numerical simulations are presented, and some discussions are given from the mathematical and biological viewpoints. Next, an optimal control problem is defined for the new model by introducing four control variables reducing the number of infected individuals. For the control problem, the necessary and sufficient conditions are derived and numerical simulations are given to verify the theoretical analysis.
A new class of 2m-point binary non-stationary subdivision schemes
(Springer, 2019) Ghaffar, Abdul; Baleanu, Dumitru; Ullah, Zafar; Bari, Mehwish; Nisar, Kottakkaran Sooppy; Al-Qurashi, Maysaa M.; Baleanu, Dumitru; 56389
A new class of 2m-point non-stationary subdivision schemes (SSs) is presented, including some of their important properties, such as continuity, curvature, torsion monotonicity, and convexity preservation. The multivariate analysis of subdivision schemes is extended to a class of non-stationary schemes which are asymptotically equivalent to converging stationary or non-stationary schemes. A comparison between the proposed schemes, their stationary counterparts and some existing non-stationary schemes has been depicted through examples. It is observed that the proposed SSs give better approximation and more effective results.
A New Class of 2Q-Point Nonstationary Subdivision Schemes and Their Applications
(Mdpi, 2019) Ghaffar, Abdul; Baleanu, Dumitru; Bari, Mehwish; Ullah, Zafar; Iqbal, Mudassar; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
The main objective of this study is to introduce a new class of 2q-point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs.
A new fractional exothermic reactions model having constant heat source in porous media with power, exponential and Mittag-Leffler laws
(Pergamon-elsevier Science Ltd, 2019) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Tanwar, Kumud; Baleanu, Dumitru; 56389
The present article deals with the exothermic reactions model having constant heat source in the porous media with strong memory effects. The Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional operators are used to induce memory effects in the mathematical modeling of exothermic reactions. The patterns of heat flow profiles are very essential for heat transfer in every kind of the thermal insulation. In the present investigation, we focus on the driving force problem due to the fact that temperature gradient is assumed. The mathematical equation of the problem is confined in a fractional energy balance equation (FEBE), which furnishes the temperature portrayal in conduction state having uniform heat source on steady state. The fractional Laplace decomposition technique is utilized to obtain the numerical solution of the corresponding FEBE describing the exothermic reactions. Some numerical results for the fractional exothermic reactions model are presented through graphs and tables. (C) 2019 Elsevier Ltd. All rights reserved.
A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
(Amer inst Physics, 2019) Baleanu, D.; Baleanu, Dumitru; Jajarmi, A.; Sajjadi, S. S.; Mozyrska, D.; 56389
In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined. Published under license by AIP Publishing.
A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying
(Springer, 2019) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389
The present paper deals with a new fractional SIRS-SI model describing the transmission of malaria disease. The SIRS-SI malaria model is modified by using the Caputo-Fabrizio fractional operator for the inclusion of memory. We also suggest the utilization of vaccines, antimalarial medicines, and spraying for the treatment and control of the malaria disease. The theory of fixed point is utilized to examine the existence of the solution of a fractional SIRS-SI model describing spreading of malaria. The uniqueness of the solution of SIRS-SI model for malaria is also analyzed. It is shown that the treatments have great impact on the dynamical system of human and mosquito populations. The numerical simulation of fractional SIRS-SI malaria model is performed with the aid of HATM and Maple packages to show the effect of different parameters of the treatment of malaria disease. The numerical results for fractional SIRS-SI malaria model reveal that the recommended approach is very accurate and effective.
A new fractional wavelet approach for the simultaneous determination of ampicillin sodium and sulbactam sodium in a binary mixture
(Pergamon-elsevier Science Ltd, 2006) Dinç, E; Baleanu, Dumitru; Baleanu, DB; 6981
A new application of the fractional wavelet transform (FWT) was proposed for the simultaneous determination of ampicillin (AP) and sulbactam (SB) in a pharmaceutical combination for injection. FWT approach is a new powerful tool for removing noise and irrelevant information from the absorption spectra. Cardinal information having higher peak amplitude, eliminated noise, sharp peaks with shrinking width of spectral range was obtained by the application of FWT procedure to the original absorption spectra. In this paper, FWT approach was subjected to the data vector of the UV-signals obtained from AP and SB in the wavelength range of 211.5-313.8 nm. Derivative transform was applied to the original absorption signal together with its FWT generalization. The calibration graphs for AP and SB were obtained by measuring the FWT and usual derivative amplitudes at zero-crossing points. The method validation was carried out by using the synthetic mixture analysis. Our proposed FWT approach was compared with the usual derivative spectrophotometry and chemometric methods (CLS, PCR and PLS) and a good agreement was reported. (c) 2005 Elsevier B.V. All rights reserved.
A New Hybrid Algorithm for Continuous Optimization Problem
(Elsevier Science inc, 2018) Farnad, Behnam; Baleanu, Dumitru; Jafarian, Ahmad; Baleanu, Dumitru; 56389
This paper applies a new hybrid method by a combination of three population base algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Symbiotic Organisms Search (SOS). The proposed method has been inspired from natural selection process and it completes this process in GA by using the PSO and SOS. It tends to minimize the execution time and in addition to reduce the complexity. Symbiotic organisms search is a robust and powerful metaheuristic algorithm which has attracted increasing attention in recent decades. There are three alternative phases in the proposed algorithm: GA, which develops and selects best population for the next phases, PSO, which gets experiences for each appropriate solution and updates them as well and SOS, which benefits from previous phases and performs symbiotic interaction update phases in the real-world population. The proposed algorithm was tested on the set of best known unimodal and multimodal benchmark functions in various dimensions. It has further been evaluated in, the experiment on the clustering of benchmark datasets. The obtained results from basic and non-parametric statistical tests confirmed that this hybrid method dominates in terms of convergence, execution time, success rate. It optimizes the high dimensional and complex functions Rosenbrock and Griewank up to 10(-330) accuracy in less than 3 s, outperforming other known algorithms. It had also applied clustering datasets with minimum intra-cluster distance and error rate. (C) 2017 Elsevier Inc. All rights reserved.
A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative
(Springer international Publishing Ag, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Mousalou, Asef; Rezapour, Shahram; 56389
We present a new method to investigate some fractional integro-differential equations involving the Caputo-Fabrizio derivation and we prove the existence of approximate solutions for these problems. We provide three examples to illustrate our main results. By checking those, one gets the possibility of using some discontinuous mappings as coefficients in the fractional integro-differential equations.
A New Numerical Algorithm For Fractional Fitzhugh-Nagumo Equation Arising in Transmission of Nerve Impulses
(Springer, 2018) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; 56389
The principal objective of this study is to present a new numerical scheme based on a combination of q-homotopy analysis approach and Laplace transform approach to examine the Fitzhugh-Nagumo (F-N) equation of fractional order. The F-N equation describes the transmission of nerve impulses. In order to handle the nonlinear terms, the homotopy polynomials are employed. To validate the results derived by employing the used scheme, we study the F-N equation of arbitrary order by using the fractional reduced differential transform scheme. The error analysis of the proposed approach is also discussed. The outcomes are shown through the graphs and tables that elucidate that the used schemes are very fantastic and accurate.
A new quadrature routine for improper and oscillatory integrals
(Elsevier Science inc, 2007) Sermutlu, E.; Sermutlu, Emre; Eyyuboglu, H. T.; 17647; 7688
In MATLAB environment, a new quadrature routine based on Gaussian quadrature rule has been developed. Its performance is evaluated for improper integrals, rapidly oscillating functions and other types of functions requiring a. large number of evaluations. This performance is compared against the other quadrature routines written for MATLAB in terms of capability, accuracy and computation time. It is found that our routine rates quite favourably. (c) 2006 Elsevier Inc. All rights reserved.
A Reliable Mixed Method for Singular Integro-Differential Equations of Non-Integer Order
(Edp Sciences S A, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Darzi, Rahmat; Agheli, Ahram; 56389
It is our goal in this article to apply a method which is based on the assumption that combines two methods of conjugating collocation and multiple shooting method. The proposed method can be used to find the numerical solution of singular fractional integro-differential boundary value problems (SFIBVPs) D-upsilon y(t) + eta integral(t)(0) (t - s)(zeta-1) y(s) ds = g(t), 1 < upsilon <= 2, 0 < zeta < 1, eta is an element of R, where D-upsilon denotes the Caputo derivative of order upsilon. Meanwhile, in a separate section the existence and uniqueness of this method is also discussed. Two examples are presented to illustrate the application and further understanding of the methods.
A reliable technique for fractional modified Boussinesq and approximate long wave equations
(Springeropen, 2019) Veeresha, P.; Baleanu, Dumitru; Prakasha, D. G.; Qurashi, M. A.; Baleanu, D.; 56389
In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely the q-homotopy analysis transform method. These equations play a vital role in describing the properties of shallow water waves through distinct dispersion relation. The convergence analysis and error analysis are presented in the present investigation for the future scheme. We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to verify the accuracy. The numerical simulation is conducted to ensure the exactness of the future technique. The obtained numerical and graphical results are presented, the proposed scheme is computationally very accurate and straightforward to study and find the solution for fractional coupled nonlinear complex phenomena arising in science and technology.
Almost local stability in discrete delayed chaotic systems
(Springer, 2017) Nategh, Mehdi; Baleanu, Dumitru; Baleanu, Dumitru; Taghizadeh, Elham; Gilani, Zahra Goli
This work studies dynamic of delayed discrete chaotic systems with bounded and unbounded delays. The time lags appear in additive which is coupled with a smooth function and nonadditive forms. It has been shown that, in both additive and nonadditive cases, the primal (non-delayed) system is neutral to the bounded delay to possess an attractive fixed point. Nevertheless, if a nonadditive and unbounded delay is supposed to affect a chaotic and measure preserving system locally, then the delay function might be sensitive to initial states. A local stabilization to the dynamics of Logistic and Gaussian maps are made and creation of attractive fixed points is illustrated.
An algorithm for Hopf bifurcation analysis of a delayed reaction-diffusion model
(Springer, 2017) Kayan, S.; Merdan, H.; 49206
We present an algorithm for determining the existence of a Hopf bifurcation of a system of delayed reaction-diffusion equations with the Neumann boundary conditions. The conditions on parameters of the system that a Hopf bifurcation occurs as the delay parameter passes through a critical value are determined. These conditions depend on the coefficients of the characteristic equation corresponding to linearization of the system. Furthermore, an algorithm to obtain the formulas for determining the direction of the Hopf bifurcation, the stability, and period of the periodic solution is given by using the Poincare normal form and the center manifold theorem. Finally, we give several examples and some numerical simulations to show the effectiveness of the algorithm proposed.
An application of derivative and continuous wavelet transforms to the overlapping ratio spectra for the quantitative multiresolution of a ternary mixture of paracetamol, acetylsalicylic acid and caffeine in tablets
(Elsevier Science Bv, 2005) Dinç, E; Baleanu, Dumitru; Özdemir, A; Baleanu, D; 56389
Quantitative multi resolution of tablets and ternary mixtures of paracetamol (PAR), acetylsalicylic acid (ASP) and caffeine (CAF) having strongly overlapping spectra was accomplished by two graphical transform methods as ratio spectra first derivative-zero crossing and ratio spectra-continuous wavelet transform-zero crossing (ratio spectra CWT-zero crossing) methods. In this study, ratio spectra derivative-zero crossing and ratio spectra CWT-zero crossing methods are based on the use of transformed signals of the ratio spectra and their calibration graphs were obtained by measuring the dA/dlambda and CWT amplitudes of the ratio spectra corresponding to zero crossing points. For the comparison purpose. PLS calibration method was applied to predict the content of the same mixtures containing the subject active Compounds. The obtained calibrations were tested by using the synthetic mixtures and standard addition technique and they applied to the simultaneous determination of PAR, ASP and CAF in commercial pharmaceutical preparation. The obtained results were statistically compared with each other as well as those obtained by HPLC method and they showed good agreement. (C) 2004 Published by Elsevier B.V.

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