Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 10Citation - Scopus: 12Regularization of the Inverse Problem for Time Fractional Pseudo-Parabolic Equation With Non-Local in Time Conditions(Springer Heidelberg, 2022) Le Dinh Long; Anh Tuan Nguyen; Baleanu, Dumitru; Nguyen Duc Phuong; Long, Le Dinh; Phuong, Nguyen Duc; Nguyen, Anh TuanThis paper is devoted to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. First, we prove the problem is non-well posed and the stability of the source function. Second, by using the Modified Fractional Landweber method, we present regularization solutions and show the convergence rate between regularization solutions and sought solution are given under a priori and a posteriori choice rules of the regularization parameter, respectively. Finally, we present an illustrative numerical example to test the results of our theory.Article Citation - WoS: 14Citation - Scopus: 17On (2+1)-Dimensional Physical Models Endowed With Decoupled Spatial and Temporal Memory Indices<sup>☆</Sup>(Springer Heidelberg, 2019) Alquran, Marwan; Yousef, Feras; Momani, Shaher; Baleanu, Dumitru; Jaradat, Imad.The current work concerns the development of an analytical scheme to handle (2 + 1) -dimensional partial differential equations endowed with decoupled spatial and temporal fractional derivatives (abbreviated by (alpha,beta) -models). For this purpose, a new bivariate fractional power series expansion has been integrated with the differential transform scheme. The mechanism of the submitted scheme depends mainly on converting the (alpha,beta) -model to a recurrence-differential equation that can be easily solved by virtue of an iterative procedure. This, in turn, reduces the computational cost of the Taylor power series method and consequently introduces a significant refinement for solving such hybrid models. To elucidate the novelty and efficiency of the proposed scheme, several (alpha,beta) -models are solved and the presence of remnant memory, due to the fractional derivatives, is graphically illustrated.Article Citation - WoS: 5Citation - Scopus: 9Numerical Study of Heat Transfer in a Microchannel Equipped With the Semicircular Ribs Influenced by Slip Condition: Effects of Various Slip Coefficient and Hartmann Number(Springer Heidelberg, 2022) Alderremy, A. A.; Aly, Shaban; Tlili, Iskander; Ghaemi, Ferial; Baleanu, Dumitru; He, XinlinIn the present work, a microchannel that benefits from the simultaneous effect of slip condition and semicircular ribs was studied to boost heat transfer. A numerical method was utilized to examine the thermal and hydraulic behavior. The results reveal that the velocity is not zero since the slip condition exists in the microchannel. Furthermore, the velocity near the wall has a dramatic value when the slip length increases. Although the heat transfer is not remarkable by semicircular ribs, the magnetic field plays a vital role in boosting the heat transfer as a result of the declining thermal boundary layer. The effect of magnetic field on the heat transfer on the low Re number is not like the higher one which means as the Reynolds number (Re) varies from 10 to 90, the heat transfer goes up from 1.12 to 2.63. Furthermore, at Re = 90, a 255% enhancement is seen in the microchannel by affecting magnetic field at Hartmann number = 15. The results of slip condition claim that slip condition is introduced as the third most effective factor in rising and improving the efficiency of the microchannel. There is a 16.23% improvement in heat transfer by using slip condition in the microchannel. More importantly, the figure for heat transfer is enhanced by increasing the radius of ribs.Article Citation - WoS: 81Citation - Scopus: 83The (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, KamyarThe 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.Article Citation - WoS: 12Citation - Scopus: 17Dynamics of Multi-Point Singular Fifth-Order Lane-Emden System With Neuro-Evolution Heuristics(Springer Heidelberg, 2022) Ali, Mohamed R.; Fathurrochman, Irwan; Raja, Muhammad Asif Zahoor; Sadat, R.; Baleanu, Dumitru; Sabir, ZulqurnainThe objective of the presented communication is to examine and analyze the solutions of nonlinear multi-singular fifth-order Lane-Emden (LE) system for different scenarios by variation of shape factors settled on the equivalent design of the LE equations. The neuro-evolution based stochastic computing is explored for the numerical measures using the artificial neural networks (ANNs) models for the appropriate continuous mapping, while the learning of decision variables is conducted using the integrated meta-heuristic global search of genetic algorithms (GA) hybrid with the local search efficiency of active-set (AS) i.e., ANN-GA-AS scheme. The numerical approach ANN-GA-AS is applied efficiently for the fifth kind of nonlinear LE model and statistical calculations further validate the accuracy, robustness as well as convergence.Article Citation - WoS: 21Citation - Scopus: 22Design of Neuro-Swarming Computational Solver for the Fractional Bagley-Torvik Mathematical Model(Springer Heidelberg, 2022) Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; Guirao, Juan L. G.This study is to introduce a novel design and implementation of a neuro-swarming computational numerical procedure for numerical treatment of the fractional Bagley-Torvik mathematical model (FBTMM). The optimization procedures based on the global search with particle swarm optimization (PSO) and local search via active-set approach (ASA), while Mayer wavelet kernel-based activation function used in neural network (MWNNs) modeling, i.e., MWNN-PSOASA, to solve the FBTMM. The efficiency of the proposed stochastic solver MWNN-GAASA is utilized to solve three different variants based on the fractional order of the FBTMM. For the meticulousness of the stochastic solver MWNN-PSOASA, the obtained and exact solutions are compared for each variant of the FBTMM with reasonable accuracy. For the reliability of the stochastic solver MWNN-PSOASA, the statistical investigations are provided based on the stability, robustness, accuracy and convergence metrics.Article Citation - WoS: 12Citation - Scopus: 13Transmission Dynamics of a Novel Fractional Model for the Marburg Virus and Recommended Actions(Springer Heidelberg, 2023) Baleanu, Dumitru; Kumar, Sachin; Singh, Jaskirat Pal; Abdeljawad, ThabetMarburg virus disease is a particularly virulent illness that causes hemorrhagic fever and has a fatality rate of up to 88%. It belongs to the same family of pathogens as the Ebola virus. The disease was first identified in 1967 as a result of two significant epidemics that happened concurrently in Marburg, hence the name Marburg, Frankfurt, both in Germany, and Belgrade, Serbia. This work proposes a unique fractional model for the Marburg virus based on the Atangana-Baleanu derivative in the Caputo sense. For the model, two equilibrium states have been founded: endemic equilibrium and disease-free equilibrium. If R-0 < 1, Castillo's method and the next-generation matrix are used to demonstrate the disease-free equilibrium's asymptotic global stability. When R-0 > 1, the endemic equilibrium point is locally asymptotically stable, according to the linearization. The model's basic reproduction rates for both humans and bats are calculated using the parameter values. Fixed point theory is used to demonstrate the solution's existence and uniqueness. Number of infected bats should be controlled and interaction with just recovered individuals should be avoided as these are the main contributors in the infection rate. These recommended actions will make the infected persons in the humans disappear, as demonstrated by the model's numerical simulations.Article Citation - WoS: 16Citation - Scopus: 17Quadratic and Cubic Logistic Models Involving Caputo-Fabrizio Operator(Springer Heidelberg, 2023) Baleanu, Dumitru; Al-Mdallal, Qasem M.; Saad, Khaled M.; Al Fahel, SaraIn this paper, we numerically investigate the fractional quadratic and cubic logistic models involving the Caputo-Fabrizio operator. We construct the successive iterations using the theory of fractional calculus and Lagrange polynomials. Then, we handled the exact solutions of these models. The validity of the accuracy and efficiency will be satisfied through some numerical results.Article Citation - WoS: 23Citation - Scopus: 21Numerical Solution of a New Mathematical Model for Intravenous Drug Administration(Springer Heidelberg, 2024) Shiri, Babak; Perfilieva, Irina; Baleanu, Dumitru; Alijani, ZahraWe develop and analyze a new mathematical model for intravenous drug administration and the associated diffusion process. We use interval analysis to obtain a system of weakly singular Volterra integral equations over ordinary functions. We then use the operational method based on Chebyshev polynomials for obtaining an approximate solution of the numerical form. We show that for a certain class of fuzzy number valued functions, their generalized Hukuhara derivatives can be reduced to the derivatives of ordinary real-valued functions. By using our approach, we are able to estimate numerical solutions very accurately.Article Citation - WoS: 24Citation - Scopus: 32Advanced Exact Solutions To the Nano-Ionic Currents Equation Through Mts and the Soliton Equation Containing the Rlc Transmission Line(Springer Heidelberg, 2023) Miah, M. Mamun; Iqbal, M. Ashik; Alshehri, Hashim M.; Baleanu, Dumitru; Osman, M. S.; Chowdhury, M. AkherIn this study, the double (G '/G, 1/G)-expansion method is utilized for illustrating the improved explicit integral solutions for the two of nonlinear evolution equations. To expose the importance and convenience of our assumed method, we herein presume two models, namely the nano-ionic currents equation and the soliton equation. The exact solutions are generated with the aid of our proposed method in such a manner that the solutions involve to the rational, trigonometric, and hyperbolic functions for the first presumed nonlinear equation as well as the trigonometric and hyperbolic functions for the second one with meaningful symbols that promote some unique periodic and solitary solutions. The method used here is an extension of the (G '/G)-expansion method to rediscover all known solutions. We offer 2D and 3D charts of the various recovery solutions to better highlight our findings. Finally, we compared our results with those of earlier solutions.