Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Optimal Control for a Variable-Order Diffusion-Wave Equation With a Reaction Term; a Numerical Study(Elsevier B.V., 2024) Megahed, F.; Shatta, S.A.; Baleanu, D.; Sweilam, N.H.In this paper, optimal control for a variable-order diffusion-wave equation with a reaction term is numerically studied, where the variable-order operator is defined in the sense of Caputo proportional constant. Necessary optimality conditions for the control problem are derived. Existence and uniqueness for the solutions of fractional optimal control problem are derived. The nonstandard weighted average finite difference method and the nonstandard leap-frog method are developed to study numerically the proposed problem. Moreover, the stability analysis of the methods is proved. Finally, in order to characterise the memory property of the proposed model, three test examples are given. It is found that the nonstandard weighted average finite difference method can be applied to study such variable-order fractional optimal control problems simply and effectively. © 2024 The Author(s)Article Citation - Scopus: 15An Exploration of Heat and Mass Transfer for Mhd Flow of Brinkman Type Dusty Fluid Between Fluctuating Parallel Vertical Plates With Arbitrary Wall Shear Stress(Elsevier B.V., 2024) Ali, G.; Kumam, P.; jarad, F.; khan, D.An equitably complex phenomenon, the Brinkman-type dusty fluid and wall shear stress effect, is utilized in various engineering and product-making fields. For instance, dusty fluids are employed in nuclear-powered reactors and gas freezing systems to reduce heat of the system. To ascertain the impact of wall shear stress on Brinkman-type dusty fluid flow, the current study intends to do so. Base on this motivation, this paper discusses the two-phase MHD fluctuating flow of a Brinkman-type dusty fluid along with heat and mass transport. Two parallel non-conducting plates are used to model the flow, one at rest and the other in motion. Heat and mass transfer, along with wall share stress, are also taken into consideration, and plate fluctuation allows the flow to occur. The Poincaré-Lighthill fluctuation method was utilised in the process to investigate systematic solutions. The findings were achieved and plotted on a graph. The two-phase flow model is created by independently simulating the fluid and dust particle equations. The effect of relevant aspects such as the Grashof number, magnetic parameter, heat flux, and dusty fluid variable on the base fluid velocity has been explored. It was found that as the magnetic flux and imposed shear force decrease, the velocity of the base fluid increases. Additionally estimated in tabular form are rate of heat transfer and skin friction, two crucial fluid parameters for engineers. According to the graphical analysis, the Brinkman kind dusty fluid has better control over dust particle and fluid velocity rather than viscous fluid. By adjusting the value of N, you may control the temperature profile. Also, by adjusting the value of Sc and γ, you may control the concentration profile. © 2023 The AuthorsArticle Citation - Scopus: 26Search for Adequate Closed Form Wave Solutions To Space–time Fractional Nonlinear Equations(Elsevier B.V., 2021) Akbar, M.A.; Seadawy, A.R.; Baleanu, D.; Roy, R.The nonlinear space–time fractional Phi-4 equation and density dependent fractional reaction–diffusion equation (FRDE) are important models to interpret the fusion and fission phenomena ensued in solid state physics, plasma physics, chemical kinematics, astrophysical fusion plasma, electromagnetic interactions etc. In this study, we search advanced and wide-ranging wave solutions to the formerly reported nonlinear fractional evolution equations in diverse family through the new generalized (G′∕G)-expansion technique. The solutions are developed with trigonometric, hyperbolic, exponential and rational functions including parameters. The technique is a compatible, functional and effective scientific scheme to examine diverse space–time fractional models in physics and engineering concerned with the real life problems. © 2021 The AuthorsArticle Citation - WoS: 44Citation - Scopus: 60Numerical Solution of 3D Rotating Nanofluid Flow Subject To Darcy-Forchheimer Law, Bio-Convection and Activation Energy(Elsevier B.V., 2022) Tayyab, Muhammad; Siddique, Imran; Jarad, Fahd; Ashraf, Muhammad Kamran; Ali, BaghThis work discourses the dynamics of three dimensional rotating nanofluid flows subject to magnetohydrodynamic, Darcy-Forchheimer law, bioconvection self-motive microorganism, and activation energy. The numerical procedure is indicated when close agreement of the current finding is attained in comparison with the existing ones as limiting case. The leading equations based on preservation of mass, momentum, and energy are formulated with partial derivatives which are then transmuted into dimensionless differential form with the enactment of apposite similarity transformations. So, to tackle the non-linearity of these equations, numerical procedure based on shooting technique and Runge-Kutta method is bound to be coded on MATLAB platform. The emerging parameters are varied to observe the change of microorganism distribution, velocity, concentration of nano species, and temperature distribution. Results are displayed graphically and discussed. It is noticed that liquid velocity is decelerated against the constraints of inertia and porosity. The temperature field is strengthened with thermophoresis and Brownian motion. The concentrations of nanoparticle and microorganism are depreciated against Lewis number and bio-Lewis number respectively. The concentration of microorganism is improved for greater peclet number Pe but it lessens with growth in bioconvection Lewis numberLb. The function 8(i) and rp(i) showed increasing response to thermophoresis parameter Nt. The parameter of Brownian motion has noticeable growing impact on concentration of nano particles but decreasing Nb for 8(i) temperature.Article Citation - Scopus: 103Dynamical Behavior of Solitons of the Perturbed Nonlinear Schrödinger Equation and Microtubules Through the Generalized Kudryashov Scheme(Elsevier B.V., 2022) Wazwaz, A.-M.; Mahmud, F.; Baleanu, D.; Roy, R.; Barman, H.K.; Osman, M.S.; Ali Akbar, M.The perturbed nonlinear Schrödinger (NLS) equation and the nonlinear radial dislocations model in microtubules (MTs) are the underlying frameworks to simulate the dynamic features of solitons in optical fibers and the functional aspects of microtubule dynamics. The generalized Kudryashov method is used in this article to extract stable, generic, and wide-ranging soliton solutions, comprising hyperbolic, exponential, trigonometric, and some other functions, and retrieve diverse known soliton structures by balancing the effects of nonlinearity and dispersion. It is established by analysis and graphs that changing the included parameters changes the waveform behavior, which is largely controlled by nonlinearity and dispersion effects. The impact of the other parameters on the wave profile, such as wave speed, wavenumber, etc., has also been covered. The results obtained demonstrate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable soliton solutions to nonlinear evolution equations emerging in various branches of scientific, technological, and engineering domains. © 2022 The Author(s)Article Citation - Scopus: 49Numerical Solution of Maxwell-Sutterby Nanofluid Flow Inside a Stretching Sheet With Thermal Radiation, Exponential Heat Source/Sink, and Bioconvection(Elsevier B.V., 2023) Farooq, U.; Waqas, H.; Imran, M.; Noreen, S.; Akgül, A.; Abbas, K.; Alharbi, K.A.M.A Survey of literature illustrates that nano liquid is further helpful for heat transportation as compared to regular liquid. Nonetheless, there are considerable gaps in our understanding of existing approaches for enhancing heat transmission in nanofluids, necessitating comprehensive research of these fluids. The current approach proposes to investigate the influence of a Maxwell-Sutterby nanofluid on a sheet while accounting for heat radiation. This paper investigates activation energy, and exponential heat source/sink. Bioconvection and motile microorganisms with Brownian motion and thermophoresis effects are considered.y linked similarity transformations, the boundary layer set of controlling partial differential equations are transformed into ordinary differential equations. A numerical strategy (shooting technique) is used to handle the transformed system of ordinary differential equations through the Bvp4c solver of the computing tool MATLAB. The results for velocity and temperature, concentration, and motile microbe profiles are numerically and graphically examined for various parameters. The velocity distribution profile decreased as the magnetic parameter varied, but increased when the mixed convection parameter increased in magnitude. The heat flux profile is improved with higher estimations of the Biot number and thermophoresis parameter. When the Prandtl number and the Brownian motion parameter's values rise, the energy profile falls. When the Peclet number and bioconvection Lewis number increased, the profile of mobile microorganisms dropped. © 2023Article Citation - Scopus: 31Numerical Framework of Hybrid Nanofluid Over Two Horizontal Parallel Plates With Non-Linear Thermal Radiation(Elsevier B.V., 2023) Waqas, H.; Noreen, S.; Imran, M.; Akgül, A.; Baleanu, D.; Galal, A.M.; Farooq, U.Significance of study: High combustion temperatures necessitate appropriate cooling systems in the combustion process. Regenerative cooling is used in the majority of chambers in liquid propellant engines. The addition of nanoparticles to the cooling fluid is a novel technique to increase the efficiency of heat transfer in the regenerative cooling process. Aim of the study: In this investigation, we investigate the two-dimensional flow of the hybrid nanofluid with suction/injection effect over two horizontal parallel plates. The non-linear thermal radiation effect is measured in the model of a hybrid nanofluid. Here we use single-walled carbon nanotubes, multi-walled carbon nanotubes, nickel-zinc iron oxide, and manganese zinc iron oxide with base fluid engine oil. The effects of different shape factors (Sphere, Bricks, Cylinder, Platelets, Column, and Lamina)are also incorporated. Research methodology: Using appropriate similarity transformations, the controlling partial differential equations are transformed into ordinary differential equations. Using the shooting strategy, the transformed higher-order ordinary differential equations are converted to first-order ordinary differential equations, and the Bvp4c built-in function in MATLAB is used to produce the numerical and graphical results of the flow parameter. Conclusion: The velocity profile is decreased by the increasing values of the suction/injection parameter. The temperature distribution profile declined for the higher values of the temperature ratio parameter. The combination of nickel zinc iron oxide and carbon nanotube nanomaterials to engine oil as a cooling fluid enhanced the heat transfer coefficient. According to the findings, carbon nanotubes outperform nickel zinc iron oxide nanoparticles in terms of increasing heat transfer coefficient and improving regenerative cooling. © 2023 The Author(s)Article Citation - Scopus: 22Solitary Wave Solution for a Generalized Hirota-Satsuma Coupled Kdv and Mkdv Equations: a Semi-Analytical Approach(Elsevier B.V., 2020) Chakraverty, S.; Baleanu, D.; Jena, R.M.Nonlinear fractional differential equations (NFDEs) offer an effective model of numerous phenomena in applied sciences such as ocean engineering, fluid mechanics, quantum mechanics, plasma physics, nonlinear optics. Some studies in control theory, biology, economy, and electrodynamics, etc. demonstrate that NFDEs play the primary role in explaining various phenomena arising in real-life. Now-a-day NFDEs in various scientific fields in particular optical fibers, chemical physics, solid-state physics, and so forth have the most important subjects for study. Finding exact responses to these equations will help us to a better understanding of our environmental nonlinear physical phenomena. In this regard, in the present study, we have applied fractional reduced differential transform method (FRDTM) to obtain the solution of nonlinear time-fractional Hirota-Satsuma coupled KdV and MKdV equations. The novelty of the FRDTM is that it does not require any discretization, transformation, perturbation, or any restrictive conditions. Moreover, this method requires less computation compared to other methods. Computed results are compared with the existing results for the special cases of integer order. The present results are in good agreement with the existing solutions. Here, the fractional derivatives are considered in the Caputo sense. The presented method is a semi-analytical method based on the generalized Taylor series expansion and yields an analytical solution in the form of a polynomial. © 2020 Faculty of Engineering, Alexandria UniversityArticle Citation - Scopus: 25Factor Analysis Approach To Classify Covid-19 Datasets in Several Regions(Elsevier B.V., 2021) Baleanu, D.; Band, S.S.; Mosavi, A.; Mahmoudi, M.R.The aim of this research is to investigate the relationships between the counts of cases with Covid-19 and the deaths due to it in seven countries that are severely affected from this pandemic disease. First, the Pearson's correlation is used to determine the relationships among these countries. Then, the factor analysis is applied to categorize these countries based on their relationships. © 2021 The AuthorsArticle Citation - Scopus: 6Computational Solutions of Conformable Space-Time Derivatives Dynamical Wave Equations: Analytical Mathematical Techniques(Elsevier B.V., 2020) Seadawy, A.R.; Baleanu, D.; Ali, A.In this article, the instigator sets up the profuse traveling wave solutions four types of fractional nonlinear equations in the sense of conformable derivatives by using the novel form of modified mathematical technique. The constructed traveling wave solutions are articulated in terms of trigonometric, hyperbolic and exponential functions. The derived results are fruitful for the physical demonstrations of problems in mathematical physics and engineering. © 2020 The Authors