Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Revealing Fractional Effects in an Asymmetric Two-Dimensional Oscillator through Variational Mechanics(SAGE Publications Ltd, 2026) Baleanu, Dumitru; Defterli, Ozlem; Asad, Jihad; Jajarmi, Amin; AlShaikh Mohammad, Noorhan F.The present study is an application of a generalized Lagrangian-Hamiltonian approach to the analysis of an asymmetric two-dimensional harmonic oscillator with the use of the Caputo fractional derivative. Fractional Euler-Lagrange and Hamiltonian equations were systematically developed and then solved numerically using a predictor-corrector version of the Adams-Bashforth-Moulton method. The results show that decreasing the value of the fractional order (alpha) generates a form of memory-based damping within the system that transforms the classical closed orbits of phase space into spiral inward trajectories and causes the total energy of the system to decrease according to a power law, regardless of whether there are any dissipative forces in the system. It was demonstrated that both the degree of coupling and the degree of asymmetry can cause the system to lose energy at different rates and to have different amounts of attenuation in each direction. It was also demonstrated that the model provides a smooth transition to classical conservative behavior as alpha approaches unity, which confirms the physical validity of this representation. This demonstrates that fractional variational mechanics provides a consistent and physically meaningful way to describe the transition from conservative to dissipative behavior for coupled oscillating systems that are governed by memory and non-local effects.Erratum RETRACTION: Solar Radiation Effect on PCM Performance in the Building Applications: The Collector Energy-Saving Potential Using CF-MWCNTs and CF-GNPs(Elsevier, 2026) Mohammad Sajadi, S.; Chen, Liangliang; Baleanu, Dumitru; Alrabaiah, Hussam; Aldabesh, Abdulmajeed; Sajadi, S. Mohammad; Liu, FenghuaArticle 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.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 Explicit Commutativity and Stability Theories for Second-Order Heun's LTVSs(World Scientific Publ Co Pte Ltd, 2025) Ibrahim, Salisu; Baleanu, DumitruThis paper derived and proved the simplex explicit commutativity theories and conditions for second-order linear time-varying systems (LTVSs) with both zero and nonzero initial conditions (ICs). We consider Heun's LTVS as a case study to verify the explicit commutative results, which were supported by simulation. Furthermore, we investigate the sensitivity of Heun's LTVS, the robustness of Heun's LTVS, the stability of Heun's LTVS, the effects due to disturbance on Heun's LTVS and the problem associated with commutativity of Heun's LTVS. These findings will tackle many problems related to the commutativity theory, the stability of LTVS, design and behavior of control systems, which have made an essential contribution and play a vital role in science and engineering. By considering a sinusoid of amplitude 5, bias -3 and frequency 7, with parameters c2,c1,c0 and an arbitrary choosing initial time (IT) t0 to be and also the initial states yA(0),yB(0),yA '(0),yB '(0), several quantitative results obtained by simulation show that the Heun's LTVSs AB and BA give the same output response, AB and BA are commutative under certain conditions and proved to be unstable numerically. Moreover, the quantitative results proved that the Heun's LTVSs AB and BA are very sensitive toward changes in ICs and parameters. Disturbance between the connections also affects the systems AB and BA, these give different responses as a result of tampering with the conditions, hence commutativity is not satisfied. Several examples have been given to support our fact explicitly and numerically. However, the explicit commutativity and stability for Heun's LTVS have not been in the literature yet, and this paper presents it for the first time. The results are well verified by simulation and treated with Wolfram Mathematica 11.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: 3Citation - Scopus: 3Existence Results for Block Matrix Operator of Fractional Orders in Banach Algebras(MDPI, 2019) Hashem, Hind; El-Sayed, Ahmed; Baleanu, DumitruThis paper is concerned with proving the existence of solutions for a coupled system of quadratic integral equations of fractional order in Banach algebras. This result is a direct application of a fixed point theorem of Banach algebras. Some particular cases, examples and remarks are illustrated. Finally, the stability of solutions for that coupled system are studied.Article Citation - WoS: 14Citation - Scopus: 18Existence Theory and Numerical Simulation of HIV-I Cure Model with New Fractional Derivative Possessing a Non-Singular Kernel(Springeropen, 2019) Aliyu, Aliyu Lsa; Alshomrani, Ali Saleh; Li, Yongjin; Inc, Mustafa; Baleanu, DumitruIn this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelof has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.