Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 10Citation - Scopus: 12Soliton Solutions for Non-Linear Kudryashov's Equation Via Three Integrating Schemes(Vinca inst Nuclear Sci, 2021) Mirhosseini-Alizamini, Mehdi; Baleanu, Dumitru; Rezazadeh, Hadi; Inc, Mustafa; Hussain, Majid; Arshed, Saima; Mirhosseini-Alizamini, Seyed Mehdi; Mustafa, I.N.C.This paper considers the non-linear Kudryashov's equation, that is an extension of the well-known dual-power law of refractive index and is analog to the generalized version of anti-cubic non-linearity. The model is considered in the presence of full non-linearity. The main objective of this paper is to extract soliton solutions of the proposed model. Three state-of-the-art integration schemes, namely modified auxiliary equation method, the sine-Gordon expansion method and the tanh-coth expansion method have been employed for obtaining the desired soliton solutions.Article Citation - WoS: 38Citation - Scopus: 31Prabhakar Fractional Derivative and Its Applications in the Transport Phenomena Containing Nanoparticles(Vinca inst Nuclear Sci, 2021) Zahid, Muhammad; Chu, Yu-Ming; Baleanu, Dumitru; Asjad, Muhammad ImranIn this paper, a new approach of analytical solutions is carried out on the thermal transport phenomena of Brinkman fluid based on Prabhakar's fractional derivative with generalized Fourier's law. The governing equations are obtained through constitutive relations and analytical solutions obtained via Laplace transform technique. Solutions for temperature and velocity field were analyzed through graphical description by MathCad software. The fluid properties revealed various aspects for different flow parameters as well as fractional parameter values and found important results. As a result, it is found that fluid properties can be enhanced by increasing the values of fractional parameters and can be useful in some experimental data where suitable.Article Citation - WoS: 1Citation - Scopus: 1Studying Heat Conduction in a Sphere Considering Hybrid Fractional Derivative Operator(Vinca inst Nuclear Sci, 2022) Latif, Mohamed S. Abdel; Baleanu, Dumitru; Kader, Abass H. AbdelIn this paper, the fractional heat equation in a sphere with hybrid fractional derivative operator is investigated. The heat conduction is considered in the case of central symmetry with heat absorption. The closed form solution in the form of three parameter Mittag-Leffler function is obtained for two Dirichlet boundary value problems. The joint finite sine Fourier-Laplace transform is used for solving these two problems. The dynamics of the heat transfer in the sphere is illustrated through some numerical examples and figures.Article Citation - WoS: 2Citation - Scopus: 2Study of Electro-Osmotic Nanofluid Transport for Scraped Surface Heat Exchanger With Heat Transfer Phenomenon(Vinca inst Nuclear Sci, 2021) Imran, Ali; Javeed, Shumaila; Baleanu, Dumitru; Zeb, Muhammad; Ahmad, Sohail; Waheed, AsifIn this study a novel mathematical model for electroosmotic flow for Cu-water based nanofluid with heat transfer phenomenon is reported for scraped-surface heat exchanger. The flow is initiated due to motion of lower wall of the channel and axial pressure gradient. The flow is modelled with aid of low Reynolds number and lubrication approximation theory. Exact analytical expressions are gathered for axial velocity, and stream functions for various stations of scraped-surface heat exchanger. Physical phenomenon of electro osmotic parameter are investigated on velocity profile, velocity distribution and pressure rise at edge of the blades. It is reported that electro-osmotic parameter mainly works as dragging force, it can be used to control the flow. This controlling mechanism may be helpful in mixing different materials in scraped-surface heat exchanger. Pressure rise at edge of the blades mainly rises below the blades with electro-osmotic, whereas, this profiles is suppressed for region above the blades and between the blades.Article Citation - WoS: 9Citation - Scopus: 11Fractional Model of Second Grade Fluid Induced by Generalized Thermal and Molecular Fluxes With Constant Proportional Caputo(Vinca inst Nuclear Sci, 2021) Ahmad, Mushtaq; Asjad, Muhammad Imran; Baleanu, Dumitru; Chu, Yu-MingIn this research article, the constant proportional Caputo approach of fractional derivative is applied to derive the generalized thermal and molecular profiles for flow of second grade fluid over a vertical plate. The governing equations of the prescribed flow model are reduced to dimensionless form and then solved for temperature, concentration, and velocity via Laplace transform. Further graphs of field variables are sketched for parameter of interest. Comparison between present result and the existing results is also presented graphically.Article Citation - WoS: 1Citation - Scopus: 1Fractional Heat Equation Optimized by a Chaotic Function(Vinca inst Nuclear Sci, 2021) Wazi, Mayada T.; Baleanu, Dumitru; Al-Saidi, Nadia; Ibrahim, Rabha W.In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function.Article Citation - WoS: 14Citation - Scopus: 13Exact Solutions of Stochastic Kdv Equation With Conformable Derivatives in White Noise Environment(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Ulutas, EsmaIn this article, we have considered Wick-type stochastic Korteweg de Vries (KdV) equation with conformable derivatives. By the help of white noise analysis, Hermit transform and extended G/G-expansion method, we have obtained exact travelling wave solutions of KdV equation with conformable derivatives. We have applied the inverse Hermit transform for stochastic soliton solutions and then we have shown how stochastic solutions can be presented as Brownian motion functional solutions by an application example.Article Citation - WoS: 8Citation - Scopus: 6Investigations of Non-Linear Induction Motor Model Using the Gudermannian Neural Networks(Vinca inst Nuclear Sci, 2022) Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; Sadat, Rahma; Ali, Mohamed R.; Sabir, ZulqurnainThis study aims to solve the non-linear fifth-order induction motor model (FO-IMM) using the Gudermannian neural networks (GNN) along with the optimization procedures of global search as a genetic algorithm together with the quick local search process as active-set technique (GNN-GA-AST). The GNN are executed to discretize the non-linear FO-IMM to prompt the fitness function in the procedure of mean square error. The exactness of the GNN-GA-AST is observed by comparing the obtained results with the reference results. The numerical performances of the stochastic GNN-GA-AST are provided to tackle three different variants based on the non-linear FO-IMM to authenticate the consistency, significance and efficacy of the designed stochastic GNN-GA-AST. Additionally, statistical illustrations are available to authenticate the precision, accuracy and convergence of the designed stochastic GNN-GA-AST.Article Citation - WoS: 11Citation - Scopus: 10Investigation of Electroosmosis Flow of Copper Nanoparticles With Heat Transfer Due To Metachronal Rhythm(Vinca inst Nuclear Sci, 2021) Waheed, Asif; Javeed, Shumaila; Baleanu, Dumitru; Zeb, Muhammad; Ahmad, Sohail; Imran, AliA mathematical model is explored to establish the electroosmotic flow for Cu -water nanoliquids within a ciliated symmetric micro-channel, the flow is established with aid of ciliary motion and axial pressure gradient. Nanofluid comprise of Cu as a nanofluid particles and water as base fluid. Maxwell-Garnelt model is exploited for viscosity and thermal conductivity of nanoliquid. Magnetic field is applied in the transverse direction and external electric field is enforced in the axial direction. Equations of motion are simplified for nanofluid flow in the micro channel by employing low Reynolds number and long wavelength approximation theory. Crucial exact analytical expression are gathered for electric potential, temperature profile, axial velocity, volume flux, pressure gradient, stream function, and result for pressure rise per wavelength explored numerically. The influence of crucial flow parameters on, flow behaviour, pumping phenomena, and temperature profile are thoroughly investigated.Article Citation - WoS: 10Citation - Scopus: 9Bright, Dark, and Singular Optical Soliton Solutions for Perturbed Gerdjikov-Ivanov Equation(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Kumar, Sunil; Ulutas, Esma; Mustafa, I.N.C.This study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this equation that models pulse dynamics in optical fibers. It is retrieved some bright, dark optical and singular solitons profile in the limiting cases of the Jacobi elliptic functions. The constraint conditions depending on the parameters for the existence of solitons are also presented.