Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Marangoni Boundary Layer Flow and Heat Transfer of Graphene-Water Nanofluid with Particle Shape Effects(MDPI AG, 2020) Baleanu, Dumitru; Iqbal, Azhar; Rashid, Umair; Liang, Haiyi; Abbas, Muhammad; ul Rahman, JamshidArticle Citation - WoS: 5Citation - Scopus: 5Solitary Wave Solutions To Gardner Equation Using Improved (ω(sic)/2 ) Tan 2 -Expansion Method(Amer inst Mathematical Sciences-aims, 2023) Sadaf, Maasoomah; Dawood, Mirfa; Abbas, Muhammad; Baleanu, Dumitru; Akram, GhazalaIn this study, the improved tan(Omega(sic)/2 )-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.Article Citation - WoS: 2Citation - Scopus: 3Dynamics of Unsteady Fluid-Flow Caused by a Sinusoidally Varying Pressure Gradient Through a Capillary Tube With Caputo-Fabrizio Derivative(Vinca inst Nuclear Sci, 2023) Perveen, Zahida; Zainab, Iqra; Akram, Ghazala; Abbas, Muhammad; Baleanu, Dumitru; Sadaf, MaasoomahThis paper presents a study of the unsteady flow of second grade fluid through a capillary tube, caused by sinusoidally varying pressure gradient, with fractional derivative model. The fractional derivative is taken in Caputo-Fabrizio sense. The analytical solution for the velocity profile has been obtained for non-homogenous boundary conditions by employing the Laplace transform and the finite Hankel transform. The influence of order of Caputo-Fabrizio time-fractional derivative and time parameter on fluid motion is discussed graphically.Article Citation - WoS: 20Citation - Scopus: 23Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation(Tech Science Press, 2021) Abbas, Muhammad; Baleanu, Dumitru; Iqbal, Muhammad Kashif; Riaz, Muhammad Bilal; Amin, MuhammadThis work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.Article Citation - WoS: 40Citation - Scopus: 41Numerical Treatment of Time-Fractional Klein-Gordon Equation Using Redefined Extended Cubic B-Spline Functions(Frontiers Media Sa, 2020) Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Amin, MuhammadIn this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein-Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order alpha is an element of (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme isO(h(2)+ Delta t(2-alpha)) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.Article Citation - WoS: 25Citation - Scopus: 29Marangoni Boundary Layer Flow and Heat Transfer of Graphene-Water Nanofluid With Particle Shape Effects(Mdpi, 2020) Baleanu, Dumitru; Liang, Haiyi; Abbas, Muhammad; Iqbal, Azhar; ul Rahman, Jamshid; Rashid, UmairGraphene nanofluids have attracted the attention of many researchers because of a variety of remarkable properties such as extraordinary electronic transport properties, high thermal conductivity, and large specific surface areas. This paper investigates the shape effects of nanoparticles on the Marangoni boundary layer of graphene-water nanofluid flow and heat transfer over a porous medium under the influences of the suction parameter. The graphene-water nanofluid flow was contained with various shapes of nanoparticles, namely sphere, column, platelet, and lamina. The problem is modeled in form of partial differential equations (PDES) with boundary conditions. The governing transport equations are converted into dimensionless form with the help of some suitable nondimensional variables. The solution of the problem was found numerically using the NDSolve technique of Mathematica 10.3 software. In addition, the numerical solutions were also compared with analytical results. The homotopy analysis method (HAM) is used to calculate the analytical results. The results show that lamina-shaped nanoparticles have better performance on temperature distribution while sphere-shaped nanoparticles are more efficient for heat transfer than other shapes of nanoparticles.Article Citation - WoS: 2Citation - Scopus: 3An Inverse Problem of Reconstructing the Time-Dependent Coefficient in a One-Dimensional Hyperbolic Equation(Springer, 2021) Abbas, Muhammad; Baleanu, Dumitru; Huntul, M. J.In this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank-Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.Article Citation - WoS: 34Citation - Scopus: 35A Numerical Approach of a Time Fractional Reaction-Diffusion Model With a Non-Singular Kernel(Mdpi, 2020) Abbas, Muhammad; Ali, Ajmal; Iqbal, Azhar; Baleanu, Dumitru; Akram, TayyabaThe time-fractional reaction-diffusion (TFRD) model has broad physical perspectives and theoretical interpretation, and its numerical techniques are of significant conceptual and applied importance. A numerical technique is constructed for the solution of the TFRD model with the non-singular kernel. The Caputo-Fabrizio operator is applied for the discretization of time levels while the extended cubic B-spline (ECBS) function is applied for the space direction. The ECBS function preserves geometrical invariability, convex hull and symmetry property. Unconditional stability and convergence analysis are also proved. The projected numerical method is tested on two numerical examples. The theoretical and numerical results demonstrate that the order of convergence of 2 in time and space directions.Article Citation - WoS: 52Citation - Scopus: 57A Numerical Investigation of Caputo Time Fractional Allen-Cahn Equation Using Redefined Cubic B-Spline Functions(Springer, 2020) Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Khalid, NaumanWe present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate solution of time fractional Allen-Cahn equation (ACE). We discretize the time fractional derivative of order alpha is an element of (0,1] by using finite forward difference formula and bring RCBS functions into action for spatial discretization. We find that the numerical scheme is of order O(h2+Delta t2-alpha) and unconditionally stable. We test the computational efficiency of the proposed method through some numerical examples subject to homogeneous/nonhomogeneous boundary constraints. The simulation results show a superior agreement with the exact solution as compared to those found in the literature.Article Citation - WoS: 32Citation - Scopus: 39A Novel 2-Stage Fractional Runge-Kutta Method for a Time-Fractional Logistic Growth Model(Hindawi Ltd, 2020) Baleanu, Dumitru; Riaz, Muhammad Bilal; Abbas, Muhammad; Arshad, Muhammad SarmadIn this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge-Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge-Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.