WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article A Class of Time-Fractional Dirac Type Operators(Pergamon-Elsevier Science Ltd, 2021) Baleanu, Dumitru; Restrepo, Joel E.; Suragan, DurvudkhanBy using a Witt basis, a new class of time-fractional Dirac type operators with time-variable coefficients is introduced. These operators lead to considering a wide range of fractional Cauchy problems. Solutions of the considered general fractional Cauchy problems are given explicitly. The representations of the solutions can be used efficiently for analytic and computational purposes. We apply the obtained representation of a solution to recover a variable coefficient solution of an inverse fractional Cauchy problem. Some concrete examples are given to show the diversity of the obtained results. (c) 2020 Elsevier Ltd. All rights reserved.Article Citation - WoS: 43On Fractional-Order Symmetric Oscillator With Offset-Boosting Control(Vilnius Univ Press, 2022) Xu, Changjin; Rahman, Mati Ur; Baleanu, DumitruThis article analyzes the dynamical evolution of a three-dimensional symmetric oscillator with a fractional Caputo operator. The dynamical properties of the considered model such as equilibria and its stability are also presented. The existence results and uniqueness of solutions for the suggested model are analyzed using the tools from fixed point theory. The symmetric oscillator is analyzed numerically and graphically with various fractional orders. It is observed that the fractional operator has a significant impact on the evolution of the oscillator dynamics showing that the system has a limit-cycle attractor. Offset-boosting control phenomena in the system are also studied with different orders and parameters.Article Citation - WoS: 30Citation - Scopus: 31Heat and Mass Transport Impact on MHD Second-Grade Fluid: A Comparative Analysis of Fractional Operators(Wiley, 2021) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Akgul, Ali; Saeed, Syed Tauseef; Baleanu, DumitruThe effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in different fields, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of magnetohydrodynamic (MHD) unsteady second-grade fluid in the presence of ramped conditions. The new governing equations of MHD second-grade fluid have been fractionalized by means of singular and nonsingular differentiable operators. To have an accurate physical significance of imposed conditions on the geometry of second-grade fluid, the constant concentration with ramped temperature and ramped velocity is considered. The fractional solutions of temperature, concentration, and velocity have been investigated by means of integral transform and inversion algorithm. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect.Article Citation - WoS: 1Citation - Scopus: 2Testing the Equality of Several Independent Stationary and Non-Stationary Time Series Models with Fractional Brownian Motion Errors(Elsevier, 2021) Mahmoudi, Mohammad Reza; Baleanu, Dumitru; Qasem, Sultan Noman; Mosavi, Amirhosein; Band, Shahab S.; S. Band, ShahabThis work is devoted to apply the parametric and nonparametric techniques to construct test of hypothesis about the equality of the probabilistic behaviors of several time series models with fractional Brownian motion errors fitted on several independent datasets. The accuracy and power of the introduced method are studied using the simulated and real datasets. The results indicate that the introduced approach is more powerful than other alternative approaches, in non-stationary cases. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Article Citation - WoS: 180Citation - Scopus: 192On Fractional Calculus with General Analytic Kernels(Elsevier Science Inc, 2019) Fernandez, Arran; Ozarslan, Mehmet Ali; Baleanu, DumitruMany possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions. We demonstrate, under some assumptions, how all of these modifications can be considered as special cases of a single, unifying, model of fractional calculus. We provide a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann-Liouville fractional integral operator. We also consider inversion properties of the new operators, prove analogues of the Leibniz and chain rules in this model of fractional calculus, and solve some fractional differential equations using the new operators. (C) 2019 Elsevier Inc. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 7Spectral Method Based on Bernstein Polynomials for Coupled System of Fredholm Integral Equations(Ministry Communications & High Technologies Republic Azerbaijan, 2016) Alipour, Mohsen; Baleanu, Dumitru; Baleanu, Dumitru; Karimi, Kobra; MatematikIn this paper, we apply Bernstein basis to solve the coupled system of Fredholm integral equations (CSFIE). This method transforms the problem to a system of linear algebraic equations that easily solvable. On the other hand, convergence analysis of this method is discussed. the examples show that the proposed method is implemented very simple and the results have high accuracy.Article Citation - WoS: 98Citation - Scopus: 112Analysis and Some Applications of a Regularized Ψ-Hilfer Fractional Derivative(Elsevier, 2022) Jajarmi, Amin; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Nieto, Juan J.The main purpose of this research is to present a generalization of Psi-Hilfer fractional derivative, called as regularized Psi-Hilfer, and study some of its basic characteristics. In this direction, we show that the psi-Riemann-Liouville integral is the inverse operation of the presented regularized differentiation by means of the same function psi. In addition, we consider an initial-value problem comprising this generalization and analyze the existence as well as the uniqueness of its solution. To do so, we first present an approximation sequence via a successive substitution approach; then we prove that this sequence converges uniformly to the unique solution of the regularized Psi-Hilfer fractional differential equation (FDE). To solve this FDE, we suggest an efficient numerical scheme and show its accuracy and efficacy via some real-world applications. Simulation results verify the theoretical consequences and show that the regularized Psi-Hilfer fractional mathematical system provides a more accurate model than the other kinds of integer- and fractional-order differential equations. (C) 2022 Elsevier B.V. All rights reserved.Article Stability Analysis and Solutions of Fractional Boundary Value Problem on the Cyclopentasilane Graph(Cell Press, 2024) Wang, Guotao; Yuan, Hualei; Baleanu, DumitruThe study is being applied to a model involving silane and on cyclopentasilane graph. We consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of cyclopentasilane. In this paper, we first study the existence of solutions to fractional conformable boundary value problem on the cyclopentasilane graph by applying Scheafer and Krasnoselskii fixed point theorems. Furthermore, we investigate different kinds of Ulam stability such as Ulam-Hyers stable, generalized Ulam-Hyers stable, Ulam-Hyers-Rassias stable and generalized Ulam-HyersRassias stable for the given problem. Finally, we give an example to support our important results.Correction The Hesitant Pythagorean Fuzzy Electre Iii: an Adaptable Recycling Method for Plastic Materials (Vol 291, 125281, 2021)(Elsevier Sci Ltd, 2024) Geetha, Selvaraj; Narayanamoorthy, Samayan; Kureethara, Joseph Varghese; Baleanu, Dumitru; Kang, DaekookArticle Citation - WoS: 1A New Formulation and Analytical Applications of Fractional Operators(World Scientific Publ Co Pte Ltd, 2024) Mehmood, Ahsan; Samraiz, Muhammad; Liu, Zhi-Guo; Baleanu, Dumitru; Vivas-Cortez, MiguelThis research paper introduces a novel formulation of the modified Atangana-Baleanu (AB) Fractional Operators (FrOs). The paper begins by discussing the boundedness of the novel fractional derivative operator. Some fractional differential equations corresponding to different choices of functions as well as comparative graphical representations of a function and its derivative are provided. Furthermore, the paper investigates the generalized Laplace transform for this newly introduced operator. By employing the generalized Laplace transform, a wide range of fractional differential equations can be effectively solved. Additionally, the paper establishes the corresponding form of the AB Caputo fractional integral operator, examines its boundedness and obtains its Laplace transform. It is worth noting that the FrOs previously documented in the existing literature can be derived as special cases of these recently explored FrOs.