Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 19Citation - Scopus: 18New Results for Multidimensional Diffusion Equations in Fractal Dimensional Space(Editura Acad Romane, 2016) Ma, Min; Baleanu, Dumitru; Baleanu, Dumitru; Gasimov, Yusif S.; Yang, Xiao-Jun; MatematikThe multidimensional diffusion equations in fractal dimensional space started to play an important role in physics. In this paper we present the analytical solutions of the multidimensional diffusion equations in fractal dimensional spaces by using the method of separation of variables. The graphs of the exact solutions are presented and the accuracy and efficiency of the approach are revealed for a class of local fractional partial differential equations.Article Citation - WoS: 34Citation - Scopus: 36New Analytical Solutions for Klein-Gordon and Helmholtz Equations in Fractal Dimensional Space(Editura Acad Romane, 2017) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Gao, Feng; MatematikWe consider the local fractional Klein Gordon equation and Helmholtz equation in (1+1) fractal dimensional space. The local fractional Laplace series expansion method is used to solve the local fractional partial differential equations in fractal dimensional space. We present the non differentiable analytical solutions and the corresponding graphs. The obtained results illustrate the accuracy and efficiency of this approach to local fractional partial differential equations.Article Citation - WoS: 12Citation - Scopus: 17Thermal and Concentration Diffusion Impacts on Mhd Maxwell Fluid: a Generalized Fourier's and Fick's Perspective(Elsevier, 2022) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Atangana, Abdon; Jarad, Fahd; Awrejcewicz, JanIn this article, a new approach to study the fractionalized Maxwell fluid is described by the Prabhakar fractional derivative near an exponentially accelerated vertical plate together with exponentially variable velocity, energy and mass diffusion through a porous media is critically examined. The phenomena has been described in forms of partial differential equations along with heat and mass transportation effect taken into account. The Prabhakar fractional operator which was recently introduced is used in this work together with generalized Fick's and Fourier's law. The fractionalized model is transfromed into non-dimensional form by using some suitable dimensionless quantities. The non-dimensional developed fractional model for momentum, thermal and diffusion equations based on Prabhakar fractional operator has been solved analytically via Laplace transformation method and calculated solutions expressed in terms of Mittag-Leffler special functions. Graphical demonstration are made to characterized the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, for results validation, comparative study among limiting models derived from fractionalized Prabhakar Maxwell fluid such as fractional and classical fluid models for Maxwell and Newtonian are performed. Further, it is observed from the graphs the valocity curves for classical fluid models relatively higher as compared to fractional fluid models, and fractional approach is more realistic and convenient as compared to classical approach.Article Citation - WoS: 20Citation - Scopus: 20The Fractional Wave Propagation, Dynamical Investigation, and Sensitive Visualization of the Continuum Isotropic Bi-Quadratic Heisenberg Spin Chain Process(Elsevier, 2022) Jarad, Fahd; Faridi, Waqas Ali; Asjad, Muhammad ImranThis paper deals with the Lakshmanan-Porsezian-Daniel equation which delineates the continuum isotropic bi-quadratic Heisenberg spin chain phenomenon. A new auxiliary equation method is exerted on the considered equation to find solitary wave profiles. It is a simple and powerful approach for developing innovative wave profiles based on diverse soliton families such as trigonometric functions, rational, hyperbolic trigonometric function and exponential function etc. As a result, the solitonic wave patterns attain such as dark, bright, dark -bright, singular, rational, periodic-singular, exponential, and periodic solitons etc. The deep dynamical aspects of the governing model study by performing the chaos and sensitivity analysis. The planer dynamical system of equation develop and satisfy the Hamiltonian criteria to assure that, the developed system is Hamiltonian dynamical system and contains all traveling wave structures and the system is conservative. The graphical explanation of energy levels presents the significant insights and the existence of closed-form solutions to the model. The periodic, quasi-periodic, and quasi-periodic-chaotic profiles are present to see the deep dynamics of the continuum isotropic bi-quadratic Heisenberg spin chain system. The graphically visualization for sensitivity analysis of the governing equation portraits by taking some initial values to verify its dependence. It is shown that, the model is more sensitive regarding to initial conditions rather then parameters. The graphical two dimensional, three dimensional, and contour visualization of the obtained results are presented to express the pulse propagation behavior by assuming the appropriate values of the involved parameters. The impact of fractional parameter is displayed in the graphical sense. The fractional order controls the soliton behaviour which means that, the prediction and precautions can be constructed about the physical phenomenon of the continuum isotropic bi-quadratic Heisenberg spin chain. As a results, the fractional order exhibits the states of distortion in continuum bi-quadratic magnetic system with non-zero vector on which the form evaluates to zero. The graphical two dimensional, three dimensional, and contour visualization of the obtained results are presented to express the pulse propagation behavior by assuming the appropriate values of the involved parameters.Article Citation - Scopus: 19Mittag-Leffler Form Solutions of Natural Convection Flow of Second Grade Fluid With Exponentially Variable Temperature and Mass Diffusion Using Prabhakar Fractional Derivative(Elsevier Ltd, 2022) Awrejcewicz, J.; Riaz, M.B.; Jarad, F.; Rehman, A.U.In this article, heat source impact on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer second grade fluid near an exponentially accelerated vertical plate with exponentially variable velocity, temperature and mass diffusion through a porous medium. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical second grade model, classical Newtonian model and fractional Newtonian model are recovered from Prabhakar fractional second grade fluid. Moreover, compare the results between second grade and Newtonian fluids for both fractional and classical which shows that the movement of the viscous fluid is faster than second grade fluid. Additionally, it is visualized that for both classical second grade and viscous fluid have relatively higher velocity as compared to fractional second grade and viscous fluid. © 2022 The Authors.Article Citation - WoS: 27Citation - Scopus: 30Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid With Newtonian Heating: Prabhakar Fractional Derivative Approach(Mdpi, 2022) Jarad, Fahd; Riaz, Muhammad Bilal; Shah, Zaheer Hussain; Rehman, Aziz UrIn this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as <mml:semantics>alpha</mml:semantics>, <mml:semantics>Pr</mml:semantics>, <mml:semantics>beta</mml:semantics>, <mml:semantics>Sc</mml:semantics>, <mml:semantics>Gr</mml:semantics>, <mml:semantics>gamma</mml:semantics>, and <mml:semantics>Gm</mml:semantics> are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.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: 43Citation - Scopus: 45An Exact Solution of a Casson Fluid Flow Induced by Dust Particles With Hybrid Nanofluid Over a Stretching Sheet Subject To Lorentz Forces(Taylor & Francis Ltd, 2022) Mebarek-Oudina, Fateh; Zaib, Aurang; Ishak, Anuar; Abu Bakar, Sakhinah; Sherif, El-Sayed M.; Baleanu, Dumitru; Khan, UmairThe concept of a hybrid nanofluid has piqued the interest of numerous researchers due to its potential for increased thermal properties, which results in high transfer rates. Hybrid nanofluids are used in heat transport systems such as electronic cooling, and applications in biomedical and pharmaceutical relief. Thus, the present paper inspects the impact of Lorentz forces on the Casson fluid flow of water-based Fe3O4-MWCNT hybrid nanofluid induced by dust particles from a stretching sheet. The leading PDEs are changed into ODEs by employing similarity variables and then achieving an exact solution for these transformed ODEs. The impacts of distinct physical constraints including fluid interaction particle parameter, Casson parameter, and magnetic parameter on the dust velocity and fluid velocity for normal nanofluid (Fe3O4/H2O) and hybrid nanofluid (Fe3O4-MWCNT/ H2O) are addressed in detail. The present analytic solution shows a strong correlation with earlier published numerical studies in limited cases.Article Citation - WoS: 16Citation - Scopus: 22New Approximate Analytical Technique for the Solution of Time Fractional Fluid Flow Models(Springer, 2021) Khan, Hassan; Tchier, Fairouz; Hincal, Evren; Baleanu, Dumitru; Bin Jebreen, Haifa; Farooq, Umar; Bin Jebreen, HaifaIn this note, we broaden the utilization of an efficient computational scheme called the approximate analytical method to obtain the solutions of fractional-order Navier-Stokes model. The approximate analytical solution is obtained within Liouville-Caputo operator. The analytical strategy generates the series form solution, with less computational work and fast convergence rate to the exact solutions. The obtained results have shown a simple and useful procedure to analyze complex problems in related areas of science and technology.Article Citation - WoS: 33Citation - Scopus: 36Shape Effect of Nanosize Particles on Magnetohydrodynamic Nanofluid Flow and Heat Transfer Over a Stretching Sheet With Entropy Generation(Mdpi, 2020) Baleanu, Dumitru; Iqbal, Azhar; Abbas, Muhammd; Rashid, UmairMagnetohydrodynamic nanofluid technologies are emerging in several areas including pharmacology, medicine and lubrication (smart tribology). The present study discusses the heat transfer and entropy generation of magnetohydrodynamic (MHD) Ag-water nanofluid flow over a stretching sheet with the effect of nanoparticles shape. Three different geometries of nanoparticles-sphere, blade and lamina-are considered. The problem is modeled in the form of momentum, energy and entropy equations. The homotopy analysis method (HAM) is used to find the analytical solution of momentum, energy and entropy equations. The variations of velocity profile, temperature profile, Nusselt number and entropy generation with the influences of physical parameters are discussed in graphical form. The results show that the performance of lamina-shaped nanoparticles is better in temperature distribution, heat transfer and enhancement of the entropy generation.