Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 3Citation - Scopus: 5Simpson's Method for Fractional Differential Equations With a Non-Singular Kernel Applied To a Chaotic Tumor Model(Iop Publishing Ltd, 2021) Defterli, Ozlem; Tang, Yifa; Baleanu, Dumitru; Arshad, Sadia; Saleem, IramThis manuscript is devoted to describing a novel numerical scheme to solve differential equations of fractional order with a non-singular kernel namely, Caputo-Fabrizio. First, we have transformed the fractional order differential equation to the corresponding integral equation, then the fractional integral equation is approximated by using the Simpson's quadrature 3/8 rule. The stability of the proposed numerical scheme and its convergence is analyzed. Further, a cancer growth Caputo-Fabrizio model is solved using the newly proposed numerical method. Moreover, the numerical results are provided for different values of the fractional-order within some special cases of model parameters.Article Citation - WoS: 18Citation - Scopus: 24Rotating 3d Flow of Hybrid Nanofluid on Exponentially Shrinking Sheet: Symmetrical Solution and Duality(Mdpi, 2020) Omar, Zurni; Dero, Sumera; Baleanu, Dumitru; Khan, Ilyas; Lund, Liaquat AliThis article aims to study numerically the rotating, steady, and three-dimensional (3D) flow of a hybrid nanofluid over an exponentially shrinking sheet with the suction effect. We considered water as base fluid and alumina (Al2O3), and copper (Cu) as solid nanoparticles. The system of governing partial differential equations (PDEs) was transformed by an exponential similarity variable into the equivalent system of ordinary differential equations (ODEs). By applying a three-stage Labatto III-A method that is available in bvp4c solver in the Matlab software, the resultant system of ODEs was solved numerically. In the case of the hybrid nanofluid, the heat transfer rate improves relative to the viscous fluid and regular nanofluid. Two branches were obtained in certain ranges of the involved parameters. The results of the stability analysis revealed that the upper branch is stable. Moreover, the results also indicated that the equations of the hybrid nanofluid have a symmetrical solution for different values of the rotation parameter (Omega).Article Citation - WoS: 21Citation - Scopus: 26Robust Stabilization of Fractional-Order Chaotic Systems With Linear Controllers: Lmi-Based Sufficient Conditions(Sage Publications Ltd, 2014) Kuntanapreeda, Suwat; Delavari, Hadi; Baleanu, Dumitru; Faieghi, Mohammad RezaThis paper is concerned with the problem of robust state feedback controller design to suppress fractional-order chaotic systems. A general class of fractional-order chaotic systems is considered and it is assumed that the systems' equations depend on bounded uncertain parameters. We transform the chaotic system equations into linear interval systems, and a sufficient stabilizability condition is derived in terms of linear matrix inequality (LMI). Then, an appropriate feedback gain is introduced to bring the chaotic states to the origin. Such design will result in a simple but effective controller. Several numerical simulations have been carried out to verify the effectiveness of the theoretic results.Article Citation - WoS: 25Citation - Scopus: 26Optical Solitons and Modulation Instability Analysis With (3+1)-Dimensional Nonlinear Shrodinger Equation(Academic Press Ltd- Elsevier Science Ltd, 2017) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaThis paper addresses the (3 + 1)-dimensional nonlinear Shrodinger equation (NLSE) that serves as the model to study the propagation of optical solitons through nonlinear optical fibers. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the solitary wave ansatz with Jaccobi elliptic function methods, we present the exact dark, bright and dark-bright or combined optical solitons to the model. The intensity as well as the nonlinear phase shift of the solitons are reported. The modulation instability aspects are discussed using the concept of linear stability analysis. The MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier Ltd. All rights reserved.Article Citation - WoS: 13Citation - Scopus: 13Numerical Solution of Highly Non-Linear Fractional Order Reaction Advection Diffusion Equation Using the Cubic B-Spline Collocation Method(Walter de Gruyter Gmbh, 2022) Das, Subir; Rajeev; Baleanu, Dumitru; Dwivedi, Kushal DharIn this article, the approximate solution of the fractional-order reaction advection-diffusion equation with the prescribed initial and boundary conditions is found with the help of a cubic B-spline collocation method, which is unconditionally stable and convergent. The accuracy of the scheme is validated by applying the method on four existing problems having analytical solutions and through the evaluation of the absolute errors between numerical results and the exact solutions for different particular cases. Applying the proposed method on the last two numerical problems, it is shown that the method performs better than the existing methods even for very less number of spatial and temporal discretizations. The main contribution of the article is to develop an efficient method to solve the proposed fractional order nonlinear problem and to find the effect on solute concentration graphically due to increase in the non-linearity in the diffusion term for different particular values of parameters.Article Citation - WoS: 29Citation - Scopus: 35Magnetized Flow of Cu + Al2o3 + H2o Hybrid Nanofluid in Porous Medium: Analysis of Duality and Stability(Mdpi, 2020) Omar, Zurni; Dero, Sumera; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat AliIn this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of S-c <= S and M-c <= M (S-c > S and M-c > M). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised.Article Citation - WoS: 3Citation - Scopus: 5A Mathematical Model To Optimize the Available Control Measures of(Elsevier, 2021) Nasidi, Bashir Ahmad; Baleanu, Dumitru; Saadi, Sultan Hamed; Baba, Isa AbdullahiIn the absence of valid medicine or vaccine for treating the pandemic Coronavirus (COVID-19) infection, other control strategies like; quarantine, social distancing, self- isolation, sanitation and use of personal protective equipment are effective tool used to prevent and curtail the spread of the disease. In this paper, we present a mathematical model to study the dynamics of COVID-19. We then formulate an optimal control problem with the aim to study the most effective control strategies to prevent the proliferation of the disease. The existence of an optimal control function is established and the Pontryagin maximum principle is applied for the characterization of the controller. The equilibrium solutions (DFE & endemic) are found to be locally asymptotically stable and subsequently the basic reproduction number is obtained. Numerical simulations are carried out to support the analytic results and to explicitly show the significance of the control. It is shown that Quarantine/isolating those infected with the disease is the best control measure at the moment.Article Citation - WoS: 31Citation - Scopus: 44Stability Analysis and Dual Solutions of Micropolar Nanofluid Over the Inclined Stretching/Shrinking Surface With Convective Boundary Condition(Mdpi, 2020) Omar, Zurni; Khan, Umair; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat AliThe present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative).Article Citation - WoS: 13Citation - Scopus: 13Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface(Mdpi, 2020) Omar, Zurni; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat AliIn this article, we reconsidered the problem of Aurangzaib et al., and reproduced the results for triple solutions. The system of governing equations has been transformed into the system of non-linear ordinary differential equations (ODEs) by using exponential similarity transformation. The system of ODEs is reduced to initial value problems (IVPs) by employing the shooting method before solving IVPs by the Runge Kutta method. The results reveal that there are ranges of multiple solutions, triple solutions, and a single solution. However, Aurangzaib et al., only found dual solutions. The effect of the micropolar parameter, suction parameter, and Prandtl number on velocity, angular velocity, and temperature profiles have been taken into account. Stability analysis of triple solutions is performed and found that a physically possible stable solution is the first one, while all leftover solutions are not stable and cannot be experimentally seen.Article Citation - WoS: 24Citation - Scopus: 29Convective Effect on Magnetohydrodynamic (Mhd) Stagnation Point Flow of Casson Fluid Over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions(Mdpi, 2020) Omar, Zurni; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat AliIn the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge-Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when lambda(1)= 0where lambda(1)is a mixed convection parameter andA > 0.1, and a single solution exists when lambda(1)> 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.