Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 35Citation - Scopus: 34New Optical Solitons of Conformable Resonant Nonlinear Schrodinger's Equation(de Gruyter Poland Sp Z O O, 2020) Rezazadeh, Hadi; Abazari, Reza; Khater, Mostafa M. A.; Inc, Mustafa; Baleanu, DumitruSardar subequation approach, which is one of the strong methods for solving nonlinear evolution equations, is applied to conformable resonant Schrodinger's equation. In this technique, if we choose the special values of parameters, then we can acquire the travelling wave solutions. We conclude that these solutions are the solutions obtained by the first integral method, the trial equation method, and the functional variable method. Several new traveling wave solutions are obtained including generalized hyperbolic and trigonometric functions. The new derivation is of conformable derivation introduced by Atangana recently. Solutions are illustrated with some figures.Article Citation - WoS: 3Citation - Scopus: 5Variable Stepsize Construction of a Two-Step Optimized Hybrid Block Method With Relative Stability(de Gruyter Poland Sp Z O O, 2022) Baleanu, Dumitru; Qureshi, Sania; Soomro, Amanullah; Shaikh, Asif AliSeveral numerical techniques for solving initial value problems arise in physical and natural sciences. In many cases, these problems require numerical treatment to achieve the required solution. However, in today's modern era, numerical algorithms must be cost-effective with suitable convergence and stability features. At least the fifth-order convergent two-step optimized hybrid block method recently proposed in the literature is formulated in this research work with its variable stepsize approach for numerically solving first- and higher-order initial-value problems in ordinary differential equations. It has been constructed using a continuous approximation achieved through interpolation and collocation techniques at two intra-step points chosen by optimizing the local truncation errors of the main formulae. The theoretical analysis, including order stars for the relative stability, is considered. Both fixed and variable stepsize approaches are presented to observe the superiority of the latter approach. When tested on challenging differential systems, the method gives better accuracy, as revealed by the efficiency plots and the error distribution tables, including the machine time measured in seconds.Article Citation - WoS: 5Citation - Scopus: 6Thermal Transport With Nanoparticles of Fractional Oldroyd-B Fluid Under the Effects of Magnetic Field, Radiations, and Viscous Dissipation: Entropy Generation; Via Finite Difference Method(de Gruyter Poland Sp Z O O, 2022) Asjad, Muhammad Imran; Usman, Muhammad; Kaleem, Muhammad Madssar; Baleanu, Dumitru; Muhammad, TaseerIt is a well-known fact that functional effects like relaxation and retardation of materials, and heat transfer phenomena occur in a wide range of industrial and engineering problems. In this context, a mathematical model is developed in the view of Caputo fractional derivative for Oldroyd-B nano-fluid. Nano-sized particles of copper (Cu) are used to prepare nano-fluid taking water as the base fluid. The coupled non-linear governing equations of the problem are transformed into dimensionless form. Finite difference scheme is developed and applied successfully to get the numerical solutions of deliberated problem. Influence of different physical parameters on fluid velocity profile and temperature profile are analyzed briefly. It is observed that for increasing values of fractional parameter (alpha), fluid velocity increased, but opposite behavior was noticed for temperature profile. Nusselt number (Nu) decayed for advancement in values of heat source/sink parameter (Q(0)), radiation parameter (Nr), volume fraction parameter of nano-fluid (phi), and viscous dissipation parameter (Ec). Skin friction (C-f) boosts for the increase in the values of magnetic field parameter (Ha). It can also be noticed that the extended finite difference scheme is an efficient tool and gives the accurate results of discussed problem. It can be extended for more numerous type heat transfer problems arising in physical nature with complex geometry.Article Citation - WoS: 2Citation - Scopus: 2On Periodic Solutions for Implicit Nonlinear Caputo Tempered Fractional Differential Problems(de Gruyter Poland Sp Z O O, 2024) Bouriah, Soufyane; Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, ErdalThe main goal of this article is to study the existence and uniqueness of periodic solutions for the implicit problem with nonlinear fractional differential equation involving the Caputo tempered fractional derivative. The proofs are based upon the coincidence degree theory of Mawhin. To show the efficiency of the stated result, two illustrative examples will be demonstrated.Article Citation - WoS: 3Citation - Scopus: 4Predicting Stability Factors for Rotational Failures in Earth Slopes and Embankments Using Artificial Intelligence Techniques(de Gruyter Poland Sp Z O O, 2024) Cemiloglu, Ahmed; Cao, Yingying; Sabonchi, Arkan K. S.; Nanehkaran, Yaser A.This study focuses on slope stability analysis, a critical process for understanding the conditions, durability, mass properties, and failure mechanisms of slopes. The research specifically addresses rotational-type failure, the primary instability mechanism affecting earth slopes. Identifying and understanding key factors such as slope height, slope angle, density, cohesion, friction, water pore pressure, and tensile cracks are essential for effective stabilization strategies. The objective of this study is to develop accurate predictive models for slope stability analysis using advanced intelligent techniques, including data mining mapping and complex decision tree regression (DTR). The models were validated using performance metrics such as mean absolute error (MAE), mean squared error (MSE), root mean square error (RMSE), and the coefficient of determination (R-2). Additionally, overall accuracy was assessed using a confusion matrix. The predictive model was tested on a dataset of 120 slope cases, achieving an accuracy of approximately 91.07% with DTR. The error rates for the training set were MAE = 0.1242, MSE = 0.1722, and RMSE = 0.1098, demonstrating the model's capability to effectively analyze and predict slope stability in earth slopes and embankments. The study concludes that these intelligent techniques offer a reliable approach for stability analysis, contributing to safer and more efficient slope management.Article Citation - WoS: 1Fractional Sturm-Liouville Operators on Compact Star Graphs(de Gruyter Poland Sp Z O O, 2024) Mutlu, Gokhan; Ugurlu, EkinIn this article, we examine two problems: a fractional Sturm-Liouville boundary value problem on a compact star graph and a fractional Sturm-Liouville transmission problem on a compact metric graph, where the orders alpha i {\alpha }_{i} of the fractional derivatives on the ith edge lie in ( 0 , 1 ) (0,1) . Our main objective is to introduce quantum graph Hamiltonians incorporating fractional-order derivatives. To this end, we construct a fractional Sturm-Liouville operator on a compact star graph. We impose boundary conditions that reduce to well-known Neumann-Kirchhoff conditions and separated conditions at the central vertex and pendant vertices, respectively, when alpha i -> 1 {\alpha }_{i}\to 1 . We show that the corresponding operator is self-adjoint. Moreover, we investigate a discontinuous boundary value problem involving a fractional Sturm-Liouville operator on a compact metric graph containing a common edge between the central vertices of two star graphs. We construct a new Hilbert space to show that the operator corresponding to this fractional-order transmission problem is self-adjoint. Furthermore, we explain the relations between the self-adjointness of the corresponding operator in the new Hilbert space and in the classical L 2 {L}<^>{2} space.Article Citation - WoS: 6Citation - Scopus: 8Pathological Study on Uncertain Numbers and Proposed Solutions for Discrete Fuzzy Fractional Order Calculus(de Gruyter Poland Sp Z O O, 2023) Baleanu, Dumitru; Ma, Chang-You; Shiri, BabakA pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established. The concept of maximal solution for obtaining a unique uncertain solution is introduced. The solutions of uncertain discrete relaxation equations for the integer and the fractional order are obtained. Various numerical examples are accompanied to clarify the theoretical results and study of uncertain system behavior.Article Citation - WoS: 32Citation - Scopus: 31On Parameterized Inequalities for Fractional Multiplicative Integrals(de Gruyter Poland Sp Z O O, 2024) Meftah, Badreddine; Xu, Hongyan; Jarad, Fahd; Lakhdari, Abdelghani; Zhu, Wen ShengIn this article, we present a one-parameter fractional multiplicative integral identity and use it to derive a set of inequalities for multiplicatively s s -convex mappings. These inequalities include new discoveries and improvements upon some well-known results. Finally, we provide an illustrative example with graphical representations, along with some applications to special means of real numbers within the domain of multiplicative calculus.Article Global Optimization and Applications To a Variational Inequality Problem(de Gruyter Poland Sp Z O O, 2021) Adeel, Muhammad; Aydi, Hassen; Baleanu, Dumitru; Hussain, AzharIn the present paper, we study the existence and convergence of the best proximity point for cyclic Theta-contractions. As consequences, we extract several fixed point results for such cyclic mappings. As an application, we present some solvability theorems in the topic of variational inequalities.Article Citation - WoS: 12Citation - Scopus: 21Generalized Invexity and Duality in Multiobjective Variational Problems Involving Non-Singular Fractional Derivative(de Gruyter Poland Sp Z O O, 2022) Kumar, Devendra; Alshehri, Hashim M.; Singh, Jagdev; Baleanu, Dumitru; Dubey, Ved PrakashIn this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo-Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.