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Citation - WoS: 81
Citation - Scopus: 83
The (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation: Its Solitons and Jacobi Elliptic Function Solutions
(Springer Heidelberg, 2021) Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian; Hosseini, Kamyar
The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2+1)-dimensional evolution model describing the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The intended aim is carried out by considering a specific transformation and adopting a modified version of the Jacobi elliptic expansion method. As a result, a number of solitons and Jacobi elliptic function solutions to the Heisenberg ferromagnetic spin chain equation are formally derived. Several three-dimensional plots are presented to demonstrate the dynamical features of the bright and dark soliton solutions.
Citation - WoS: 20
Citation - Scopus: 24
The (2+1)-Dimensional Hyperbolic Nonlinear Schrodinger Equation and Its Optical Solitons
(Amer inst Mathematical Sciences-aims, 2021) Hosseini, Kamyar; Salahshour, Soheil; Sadri, Khadijeh; Mirzazadeh, Mohammad; Park, Choonkil; Ahmadian, Ali; Baleanu, Umitru; Baleanu, Dumitru
A comprehensive study on the (2+1)-dimensional hyperbolic nonlinear Schrodinger (2D-HNLS) equation describing the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics is conducted in the current paper. To this end, after reducing the 2D-HNLS equation to a one-dimensional nonlinear ordinary differential (1D-NLOD) equation in the real regime using a traveling wave transformation, its optical solitons are formally obtained through a group of well-established methods such as the exponential and Kudryashov methods. Some graphical representations regarding optical solitons that are categorized as bright and dark solitons are considered to clarify the dynamics of the obtained solutions. It is noted that some of optical solitons retrieved in the current study are new and have been not retrieved previously.
Citation - WoS: 4
Citation - Scopus: 3
2d Gravity and the Hamilton-Jacobi Formalism
(Soc Italiana Fisica, 2002) Baleanu, D; Baleanu, Dumitru; Güler, Y; Matematik
Hamilton-Jacobi formalism is used to study 2D gravity and its SL(2, R) hidden symmetry. If the contribution of the surface term is considered, the obtained results coincide with those given by the Dirac and Faddeev-Jackiw approaches.
Citation - WoS: 33
Citation - Scopus: 43
A 3d Virtual Environment for Training Soccer Referees
(Elsevier Science Bv, 2019) Isler, Veysi; O'Connor, Rory V.; Clarke, Paul M.; Gulec, Ulas; Yilmaz, Murat
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 6-Point Subdivision Scheme and Its Applications for the Solution of 2nd Order Nonlinear Singularly Perturbed Boundary Value Problems
(Amer inst Mathematical Sciences-aims, 2020) Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; Mustafa, Ghulam; Anjum, Kaweeta
In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C-2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.
A comparison of iterative Fourier transform algorithms for image quality estimation
(Optical Soc Japan, 2018) Alsaka, Dina Yaqoob; Arpali, Çağlar; Arpali, Serap Altay
A comparison was established between two iterative Fourier transform algorithms (IFTAs), such as the original Gerchberg–Saxton (GS) and the mixed-region amplitude freedom (MRAF) algorithms, for the hologram reconstruction of different target images through the full reference image quality estimation (IQE) and pixel homogeneity in the Fourier plane presented theoretically and experimentally. The comparison was applied depending upon both algorithms based on a computer-generated hologram (CGH) implemented utilizing a reflective phase-modulated liquid-crystal spatial light modulator (LC-SLM) to obtain the digital kinoform holograms of the desired intensity distributions. These digital holograms were applied to reconstruct the intensity patterns for 852 nm, which represents a laser beam source. The theoretical and experimental results of the reconstructed patterns obtained using the MRAF algorithm were found to be smoother and better than the patterns obtained using the GS algorithm. Unmodulated light beam (dc term) is removed from the reconstructed patterns attributed to digital kinoform holograms of MRAF algorithm as an alternative to the theoretical and experimental results without using any additional optic equipment at the light path. Moreover, this paper discussed the full reference objective quality estimations, such as mean square error (MSE), peak signal-to-noise ratio (PSNR), structural content (SC), normalized absolute error (NAE), normalized cross correlation (NK), and homogeneity of pixels, through the contrast (Cont) and inverse difference moment (IDM) for numerical and experimental results. According to the two desired intensity distributions processed theoretically and experimentally, the results of MRAF algorithm were found to be in the highly accurate recovered phase, the quality of image was enhanced, and the dc term was decreased. Image quality estimation of full reference objective relay on the feedback algorithms experimental attestation has not been implemented yet.
A Computationally Efficient Method For a Class of Fractional Variational and Optimal Control Problems Using Fractional Gegenbauer Functions
(Editura Academiei Romane, 2018) El-Kalaawy, Ahmed A.; Doha, Eid H.; Ezz-Eldien, Samer S.; Abdelkawy, M. A.; Hafez, R. M.; Amin, A. Z. M.; Baleanu, Dumitru; Zaky, M. A.
This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.
A Gap in the Paper A Note On Cone Metric Fixed Point Theory and Its Equivalence [Nonlinear Anal. 72(5), (2010), 2259-2261]
(Gazi Univ, 2011) Abdeljawad, Thabet; Karapınar, Erdal
There is a gap in Theorem 2.2 of the paper of Du [1]. In this paper, we shall state the gap and repair it.
A Generalization of Fixed Point Result of Nonlinear Cirić Type Contraction on Suprametric Spaces
(Univ Nis, Fac Sci Math, 2025) Yalcin, Ceylan; Bilazeroglu, Seyma
In this study, the nonlinear technique: (psi,phi)-weak contraction, created by Dutta and Choudhury [6], is used to make the Ciric type contraction nonlinear. Moreover, it is demonstrated that there is unique fixed point in suprametric space for this nonlinear Ciric type contraction.
Citation - WoS: 1
Citation - Scopus: 1
A Hybrid Approach Based on Qualitative and Quantitative Techniques for Analyzing Last-Mile Parcel Delivery
(Springer India, 2025) Kanik, Zehra B.; Eriskan, Sibel; Soysal, Mehmet; Omurgonulsen, Mine
Operational excellence in last-mile delivery is becoming increasingly challenging, highlighting the need for a strategic assessment framework to improve decision-making processes. This study aims to provide a strategic assessment tool for last-mile parcel delivery processes, which are critical in terms of service levels, cost management and sustainability. The study presents a comprehensive approach to identify and prioritise feasible strategies by combining qualitative data obtained from expert opinions with Strengths, Weaknesses, Opportunities, and Threats analysis (SWOT) and Multi-Criteria Decision-Making (MCDM) methods. As a result of semi-structured interviews conducted with nine experts, 27 strategic criteria were identified and classified under SWOT dimensions. The 10 strategies developed during the interviews were evaluated by using the Intuitionistic Fuzzy Set (IFS) approach, which considers expert reliability, the Full Consistency Method (FUCOM) for weighting, and the Complex Proportional Assessment (COPRAS) technique for final ranking. There is a clear gap in the literature regarding critical criteria and strategies for last-mile delivery in developing economies. Since it is not possible to implement all strategies simultaneously due to limited resources, the strategies proposed in this study have been prioritised according to their relative importance. While expert-based evaluations in the literature typically assume that experts have equal influence, this study differs from the literature by weighting experts based on their level of experience. This approach not only addresses the gap in strategy and criterion development in the literature but also offers a more realistic and feasible approach from an implementation perspective. The findings show that all strategies are meaningful in improving last-mile performance, but their impact levels vary. "Developing public and corporate strategies for environmental sustainability" stands out as the highest priority strategy with a performance index of 100 points, while "Incorporating parcel transportation-related topics into logistics management education" is considered as the lowest priority strategy with 91.94 points. Limitations of this study arise from the niche nature of the sector and the small sample size.
A k-Dimensional System of Fractional Finite Difference Equations
(Hindawi Ltd, 2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid
We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.
A Meta-Heuristic Stochastic Algorithm for the Numerical Treatment of Cancer Model through the Chemotherapy and Stem Cells
(Elsevier, 2026) Baleanu, Dumitru; Defterli, Ozlem; Sabir, Zulqurnain; Abdelkawy, M. A.
Objective: The aim of current research is to present the numerical performances of the cancer treatment model based on chemotherapy and stem cells using one of the heuristic computing neural network procedures. The cancer treatment model through chemotherapy and stem cells is categorized into stem cells, affected cells, tumor cells, and chemotherapy-based concentration drug. Method: A process of artificial neural network is applied using the hybrid optimization of global and local search schemes, which are taken as genetic algorithm (GA) and an active set (AS). An error-based fitness function is designed by using the differential model and then optimized by the hybridization of both global and local search schemes. GA is applied to exploit the global result and give a primary guess to the AS that further improves the results locally. AS is rooted in the GA, where GA produces new populaces and AS optimizes the fitness function for every individual. The hybridization of these two schemes is used iteratively for purifying the results. Ten numbers of neurons and log-sigmoid activation functions has been used to solve the cancer treatment model based on chemotherapy and stem cells. Results: For the correctness of the stochastic solver, the obtained numerical results have been compared with any traditional scheme. Moreover, the reliability and capability of the scheme are performed through the absolute error around 10-05 to 10-07 along with different statistical approaches for solving the mathematical model. Novelty: The proposed artificial neural network structure along with the hybrid optimization of global and local search schemes has never been implemented before to solve the cancer treatment model based on chemotherapy and stem cells.
A New Classification System for Weathered Weak Rock Masses
(Techno-Press, 2026) Mao, Yimin; Nanehkaran, Yaser A.; Azarafza, Mohammad; Miao, Decheng
This research presents a new empirical rock mass classification system for sedimentary weak rocks, such as marlstones, taking into account the extent of weathering within the rock mass. For this purpose, 45 marlstone samples were systematically collected from the South Pars region in southwest Iran. The study involved measuring the geoengineering characteristics of the marls and assessing the degree of weathering they had undergone. The collected data was used to create variation weathering charts that show changes in rock mass durability and geoengineering properties with different degrees of weathering. These new charts are valuable tools for evaluating the condition of marlstone rock masses, providing a clearer understanding of how weathering affects their stability and durability. The empirical classification system introduced in this study significantly advances the assessment and management of marlstone formations in geotechnical engineering and related fields.
A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions
(Hindawi LTD, 2014) Wang, Guotao; Liu, Sanyang; Zhang, Lihong; Baleanu, Dumitru
A new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.
Citation - WoS: 5
Citation - Scopus: 6
A Review of Passive Design Strategies and Their Effect on Thermal Resilience in Low-Income Households
(Elsevier Science S.A., 2025) Kokatnur, Tejas; Ferreira, Shane; Akkoc, Busra Karadeniz; Markarian, Elin; Nojedehi, Pedram; Qiblawi, Seif; Azar, Elie
Climate change is causing more frequent and extreme weather events (e.g., heat waves and ice storms) that disproportionately impact low-income households with poor building conditions. Passive design strategies offer a promising solution to enhance building thermal resilience; however, little is known about their actual application and effectiveness in low-income households under different climate conditions. This paper presents a scoping literature review of 123 articles that evaluated passive design strategies applied to low-income housing contexts. The detailed article review shows that wall-and roof-related passive design strategies (e.g., insulation, sealing) are the most frequently studied and effective strategies, increasing comfort hours and energy savings with a wide variation of up to 24 % and 67 %, respectively. Combined strategies often outperformed individual strategies. In contrast, some studies reported unintended consequences following the adoption of passive design strategies, such as increases in energy demand reaching as high as 50 %. Such findings shed light on the need for design processes to consider multiple performance metrics, as well as behavioural and socio-economic factors that require more in-depth investigation, such as energy poverty and rebound effects. Detailed recommendations are finally provided to guide future research and applications on the topic, covering the need to (i) explore and combine underrepresented thermal resilience strategies and metrics, (ii) follow more standardized reporting practices, (iii) quantify costs and identify implementation barriers, and (iv) integrate participatory research methods to support technical assessments with contextual knowledge of the studied low-income households and communities.
A Switching Inverse Dynamics Controller for Parallel Manipulators around Drive Singular Configurations
(Tubitak Scientific & Technological Research Council Turkey, 2016) Ider, Sitki Kemal; Ozdemir, Mustafa
Despite many advantages, parallel manipulators are known to possess drive singularities where the control of one or more degrees of freedom is lost. Around these singular configurations, the required actuator forces grow unbounded. Previous efforts in the literature put forward singularity-consistent trajectory planning and singularity robust modification of the dynamic equations as a solution to this problem. However, this previous method is applicable only for the open-loop operation of the manipulator, whereas initial configuration errors, external disturbances, and modeling errors should necessarily be taken into account in a closed-loop sense in real-life applications. With this aim, a switching inverse dynamics controller is proposed in this study for the trajectory tracking control of parallel manipulators as they pass through drive singular configurations. Simulations of the application of the developed controller result in good tracking performance, even in the presence of modeling errors, while the actuator efforts remain bounded and continuous in the neighborhood of the singularity.
Citation - WoS: 5
Citation - Scopus: 7
About Fractional Calculus of Singular Lagrangians
(Fuji Technology Press Ltd, 2005) Baleanu, Dumitru
In this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. We observed that if a Lagrangian is singular in the classical sense, it remains singular after being fractionally generalized. The fractional Lagrangian is non-local but its gauge symmetry was preserved despite complexity of equations in fractional cases. We generalized four examples of singular Lagrangians admitting gauge symmetry in fractional case and found solutions to corresponding Euler-Lagrange equations.
Citation - Scopus: 5
About Fractional Calculus of Singular Lagrangians
(Institute of Electrical and Electronics Engineers Inc., 2004) Baleanu, D.; Baleanu, D.
In this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. Despite of the complexity of solutions in the fractional case the gauge classical symmetry was preserved. Four examples of fractional singular Lagrangians were analyzed in details. © 2004 IEEE.
About fractional quantization and fractional variational principles
(Elsevier, 2009) Baleanu, Dumitru
in this paper, a new method of finding the fractional Euler-Lagrange equations within Caputo derivative is proposed by making use of the fractional generalization of the classical Fad di Bruno formula. The fractional Euler-Lagrange and the fractional Hamilton equations are obtained within the 1 + 1 field formalism. One illustrative example is analyzed. (C) 2008 Elsevier B.V. All rights reserved.
Citation - WoS: 64
Citation - Scopus: 70
About Fractional Quantization and Fractional Variational Principles
(Elsevier, 2009) Baleanu, Dumitru
in this paper, a new method of finding the fractional Euler-Lagrange equations within Caputo derivative is proposed by making use of the fractional generalization of the classical Fad di Bruno formula. The fractional Euler-Lagrange and the fractional Hamilton equations are obtained within the 1 + 1 field formalism. One illustrative example is analyzed. (C) 2008 Elsevier B.V. All rights reserved.

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