Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 41Citation - Scopus: 36Exploring the Potential of Heat Transfer and Entropy Generation of Generalized Dusty Tetra Hybrid Nanofluid in a Microchannel(Elsevier, 2024) Kumam, Poom; Watthayu, Wiboonsak; Jarad, Fahd; Khan, DolatCaputo-Fabrizio time-fractional derivatives are the subject of this paper. This article generalizes the concept of dusty Tetra hybrid nanofluid moving freely via convection between infinite vertical parallel static plates. Free convection and buoyant force cause the flow and transmit the heat. In addition, there is a consistent distribution of spherical dust particles over the whole flow. It is the temperature difference between the two regions that sets off free convection. Free convection takes heat transfer into account. The dust Tetra hybrid nanofluid classical model employs nondimensional variables to achieve a dimensionless form. We also convert the dimensionally-free model into a fractional generalized dusty Tetra hybrid nanofluid model. In this paper, we use the finite sine approach to analytically solve the governing equations of the generalized Dusty Tetra hybrid nanofluid model. In this article, we generalize the concept of a dust-filled Tetra hybrid nanofluid freely flowing between infinite vertical parallel plates. We found an analytical solution to the governing equations for the generalized dusty Tetra hybrid nanofluid by combining the Finite Sine Fourier and Laplace transforms. Understanding the mechanics of velocity and temperature profiles requires the use of numerical computation for a variety of embedded factors. In-depth statistical analysis and charting of data are features of this investigation. Using Mathcad-15, we plot the profiles of the Tetra hybrid nanofluid, dust particles, and temperatures to see the findings physically. Also determined are the skin friction and Nusselt number. The rate of heat transfer decreases with time, as seen in Table 1. Similarly, as seen in Table 2, raising the fractional parameter results in a higher skin friction. In addition, the energy profile of both velocities increases with increasing tetra hybrid nano fluid volume percent, albeit the fraction's contribution decreases with time. Since the fractional models are more accurate, they also provide more potential outcomes. When all the facts are considered, these choices may out to be the best.Article Citation - WoS: 9Citation - Scopus: 10An Effective Qlm-Based Legendre Matrix Algorithm To Solve the Coupled System of Fractional-Order Lane-Emden Equations(Elsevier, 2024) Baleanu, Dumitru; Izadi, MohammadThe purpose of this study is to propose a computationally effective algorithm for the numerical evaluation of a fractional-order system of singular Lane -Emden type equations arising in physical problems. The fractional operator considered is in the sense of the Liouville-Caputo derivative. The presented matrix collocation method is based upon a combination of the quasilinearization method (QLM) and the shifted Legendre functions (SLFs) and is called QLM-SLFs method. By applying first the QLM to the nonlinear underlying system, we get a family of linear equations. Hence, a spectral matrix collocation scheme relied on the SLFs is designed to solve the resulting sequence of linear system of equations at very few iterations. The uniform convergence of the shifted Legendre expansion series solution is established. To illustrate the effectiveness of the proposed QLM-SLFs technique in the present paper, three test examples are carried out. The applicability and validity of the proposed method are testified through comparisons with the outcomes of other existing procedures in the literature. The proposed QLM-SLFs method is efficient and easy to implement. The approximation obtained by the method also converges quickly to the solutions of the underlying model problem. In comparison with available existing computational procedures, the QLM-SLFs approach shows that the use of Legendre functions together with QLM provides solutions with high accuracy and exponential convergence rate.Article Citation - WoS: 62Citation - Scopus: 70The Novel Augmented Fermatean Mcdm Perspectives for Identifying the Optimal Renewable Energy Power Plant Location(Elsevier, 2022) Parthasarathy, Thirumalai Nallasivan; Pragathi, Subramaniam; Shanmugam, Ponnan; Baleanu, Dumitru; Ahmadian, Ali; Kang, Daekook; Narayanamoorthy, SamayanThe Fermatean fuzzy set has been authorized as a suitable tool for the uncertainty and vagueness of information by augmenting the spatial space of acceptance membership and non-acceptance membership degrees of both intuitionistic and Pythagorean fuzzy sets. Solar energy does not emit any hazardous gases into the atmosphere, making it one of the most effective strategies to reduce global warming in the environment. Under a variety of circumstances, finding a spot for a photovoltaic solar power plant might be difficult. As a result, we experiment with multi-criteria decision-making (MCDM) techniques. We presented a hybrid technique based on the PV-SPSS method based on the Removal Effects of Criteria (MEREC) and Multiple Objective Optimization on the Basis of Ratio Analysis with Full Multiplicative Form (MULTIMOORA) analysis. The MEREC approach is used to calculate the weightage of each attribute, and MULTIMOORA is used to find the ranking of the alternatives. Also, a new rectified generalized score function determines the score value of FFSs. Culmination: the validity of the result is assessed by implementing the existing MCDM approaches and by changing the criterion weight.Article Citation - WoS: 16Citation - Scopus: 16The Performance of a Numerical Scheme on the Variable-Order Time-Fractional Advection-Reaction Equations(Elsevier, 2022) Hajipour, Mojtaba; Baleanu, Dumitru; Kheirkhah, FarnazThis paper is concerned with a highly accurate numerical scheme for a class of one and two-dimensional time-fractional advection-reaction-subdiffusion equations of variable order alpha(x, t) is an element of (0, 1). For the spatial and temporal discretization of the equation, a fourth order compact finite difference operator and a third-order weighted-shifted Grunwald formula are applied, respectively. The stability and convergence of the present scheme are addressed. Some extensive numerical experiments are performed to confirm the theoretical analysis and high-accuracy of this novel scheme. Comparisons are also made with the available schemes in the literature. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 2Unification and Extension of the Factorization Method for Constructing Exactly and Conditionally-Exactly Solvable Potentials. the Case of a Single Potential Generating Function(Elsevier, 2022) Nigmatullin, R. R.; Khamzin, A. A.; Baleanu, D.The article proposes a new algorithm for applying the factorization method to the problem of calculating the spectrum of exactly and conditionally exactly solvable potentials. The proposed algorithm allows us to unify and extend the capabilities of the factorization method to construct exactly solvable potentials. The new approach is demonstrated by calculating the eigenvalues of exactly solvable potentials constructed using a single function in the form of the Laurent-type polynomial. The algorithm makes it possible to significantly simplify the scheme for calculating the spectrum, parameters of the superpotential, as well as the constrain conditions for the parameters of the potential, in the case of conditionally exactly solvable potentials. It is shown that the shape of the spectrum is determined only by the differential equation, which is satisfied by the potential generating function.Article Citation - WoS: 5Citation - Scopus: 4Solar Radiation Effect on Pcm Performance in the Building Applications: the Collector Energy-Saving Potential Using Cf-Mwcnts and Cf-Gnps(Elsevier, 2022) Sajadi, S. Mohammad; Liu, Fenghua; Alrabaiah, Hussam; Aldabesh, Abdulmajeed; Baleanu, Dumitru; Chen, Liangliang; Mohammad Sajadi, S.In this study, a hot and desert location with an annual temperature of 27.1 ? and a very high radiation intensity of 2143 kWh/m(2), a solar system (ES) was approved to provide building cooling necessities. The cooling system, by connecting to the solar system, supplied a part of its required energy. The outer layer of the building walls was equipped with PCM (SP-21EK) with a melting point of 21-23 and latent heat of 170 kJ/kg. In the solar system, water was filled to absorb energy and then a combination of CF-MWCNTs and CF-GNPs nanoparticles were injected to the solar system to improve effectiveness. In July, when the radiation intensity was very high, the combination of PCM and SC condensed energy consumption (EC) by up to 46.48%. The presence of CF-MWCNTs and CF-GNPs at 0.1 wt% was useful in all conditions (2, 3 and 4 lit/min). In this case, the EC reduction was in the range of 360 to 1026 kWh. At lower concentrations, the nanoparticles not only were not worthwhile, in some cases increased EC by 937 kWh.Article Citation - WoS: 7Citation - Scopus: 7Projectile Motion Using Three Parameter Mittag-Leffler Function Calculus(Elsevier, 2022) Belgacem, Rachid; Kumar, Sunil; Baleanu, Dumitru; Djilali, Salih; Bokhari, AhmedIn the present work, we study the motion of the projectile using the regularized Prabhakar derivative of order beta. The correlation of physical quantities with units of measurement creates an obstacle in solving some fractional differential equations, as the solutions presented mathematically may not have a physical meaning. To overcome this problem and maintain dimensions of physical quantities, an auxiliary parameter sigma is usually used. We obtain analytical solutions of the velocity fractional differential system in terms of the three parameters Mittag-Leffler function denoted Ea ,beta(z). We recover the cases when applying Caputo and ordinary derivatives. (c) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.Article Citation - WoS: 7Citation - Scopus: 9The Investigation of Fe3o4 Atomic Aggregation in a Nanochannel in the Presence of Magnetic Field: Effects of Nanoparticles Distance Center of Mass, Temperature and Total Energy Via Molecular Dynamics Approach(Elsevier, 2022) Fagiry, Moram A.; Sajadi, S. Mohammad; Almasri, Radwan A.; Karimipour, Arash; Li, Zhixiong; Ghaemi, Ferial; Liu, Xinglong; Mohammad Sajadi, S.The computational procedure was utilized to explain the size effect of Fe3O4 nanoparticles on atomic behavior and phenomena of nanoparticles accumulation in nanochannel of ideal platinum (Pt) and the external magnetic field. Argon (Ar) atoms were considered as the base liquid, and the molecular dynamics procedure was utilized in this investigation. We utilized the Lennard-Jones potential to interact between the particles, whereas the nanochannel and nanoparticles structures were simulated. To compute the atomic manner, the quantities of nanoparticles distance center of mass, and the aggregation duration were presented. The outcomes implied that the nanoparticles size had a significant role in the accumulation. As the nanoparticles' size increased, the accumulation time of nanoparticles reached to 1.29 ns. Also, the outer magnetic field could severly postpone this event. (C) 2021 Published by Elsevier B.V.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.Book Citation - Scopus: 15Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems(Elsevier, 2022) Moonis, M.; Baleanu, D.; Zhang, Y.-D.; Gervasi, O.; Karaca, Y.Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. © 2022 Elsevier Inc. All rights reserved.