Matematik Bölümü

Permanent URI for this communityhttps://hdl.handle.net/20.500.12416/412

Browse

Now showing 1 - 20 of 2882

Citation - Scopus: 14
An 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 Authors
Citation - WoS: 4
Special Issue Section on Fractal Ai-Based Analyses and Applications To Complex Systems: Part I
(World Scientific Publ Co Pte Ltd, 2021) Baleanu, Dumitru; Moonis, Majaz; Muhammad, Khan; Zhang, Yu-Dong; Gervasi, Osvaldo; Karaca, Yeliz
Citation - WoS: 4
Citation - Scopus: 2
Locally Convex Valued Rectangular Metric Spaces and the Kannan's Fixed Point Theorem
(Eudoxus Press, Llc, 2012) Abdeljawad, Thabet; Abdeljawad, Thabet; Turkoglu, Duran; Matematik
Rectangular TVS-cone metric spaces are introduced and Kannan's fixed point theorem is proved in these spaces. Two approaches are followed for the proof. At first we prove the theorem by a direct method using the structure of the space itself. Secondly, we use the nonlinear scalarization used recently by Wei-Shih Du in [A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove the equivalence of the Banach contraction principle in cone metric spaces and usual metric spaces. The proof is done without any normality assumption on the cone of the locally convex topological vector space, and hence generalizing several previously obtained results.
Calculus on fractals
(2015) Golmankhaneh, Alireza K.; Baleanu, Dumitru
In this chapter we present a framework and a calculus on fractals. The suggested equation has been solved and applied in physics and dynamics.
Citation - WoS: 142
Citation - Scopus: 161
On the Existence of Solutions for Some Infinite Coefficient-Symmetric Caputo-Fabrizio Fractional Integro-Differential Equations
(Springeropen, 2017) Mousalou, Asef; Rezapour, Shahram; Baleanu, Dumitru
By mixing the idea of 2-arrays, continued fractions, and Caputo-Fabrizio fractional derivative, we introduce a new operator entitled the infinite coefficient-symmetric Caputo-Fabrizio fractional derivative. We investigate the approximate solutions for two infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential problems. Finally, we analyze two examples to confirm our main results.
Citation - WoS: 74
Citation - Scopus: 81
On the Accurate Discretization of a Highly Nonlinear Boundary Value Problem
(Springer, 2018) Jajarmi, Amin; Baleanu, Dumitru; Hajipour, Mojtaba
The aim of this manuscript is to investigate an accurate discretization method to solve the one-, two-, and three-dimensional highly nonlinear Bratu-type problems. By discretization of the nonlinear equation via a fourth-order nonstandard compact finite difference formula, the considered problem is reduced to the solution of a highly nonlinear algebraic system. To solve the derived nonlinear system, a modified nonlinear solver is used. The new scheme is accurate, fast, straightforward and very effective to find the lower and upper branches of the Bratu's problem. Numerical simulations and comparative results for the one-, two-, and three-dimensional cases verify that the new technique is easy to implement and more accurate than the other existing methods in the literature.
Citation - WoS: 12
Citation - Scopus: 12
A Computational Approach Based on the Fractional Euler Functions and Chebyshev Cardinal Functions for Distributed-Order Time Fractional 2d Diffusion Equation
(Elsevier, 2023) Heydari, M. H.; Hosseininia, M.; Baleanu, D.
In this paper, the distributed-order time fractional diffusion equation is introduced and studied. The Caputo fractional derivative is utilized to define this distributed-order fractional derivative. A hybrid approach based on the fractional Euler functions and 2D Chebyshev cardinal functions is proposed to derive a numerical solution for the problem under consideration. It should be noted that the Chebyshev cardinal functions process many useful properties, such as orthogonal-ity, cardinality and spectral accuracy. To construct the hybrid method, fractional derivative oper-ational matrix of the fractional Euler functions and partial derivatives operational matrices of the 2D Chebyshev cardinal functions are obtained. Using the obtained operational matrices and the Gauss-Legendre quadrature formula as well as the collocation approach, an algebraic system of equations is derived instead of the main problem that can be solved easily. The accuracy of the approach is tested numerically by solving three examples. The reported results confirm that the established hybrid scheme is highly accurate in providing acceptable results.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
Citation - WoS: 50
Citation - Scopus: 63
Fractional Complex Transform Method for Wave Equations on Cantor Sets Within Local Fractional Differential Operator
(Springer, 2013) Yang, Xiao-Jun; Jafari, H.; Baleanu, Dumitru; Su, Wei-Hua
This paper points out the fractional complex transform method for wave equations on Cantor sets within the local differential fractional operators. The proposed method is efficient to handle differential equations on Cantor sets.
Citation - WoS: 48
Citation - Scopus: 53
Numerical Analysis of Atangana-Baleanu Fractional Model To Understand the Propagation of a Novel Corona Virus Pandemic
(Elsevier, 2022) Butt, A. I. K.; Ahmad, W.; Rafiq, M.; Baleanu, D.
In this manuscript, we formulated a new nonlinear SEIQR fractional order pandemic model for the Corona virus disease (COVID-19) with Atangana-Baleanu derivative. Two main equilibrium points F-0*, F-1* of the proposed model are stated. Threshold parameter R-0 for the model using next generation technique is computed to investigate the future dynamics of the disease. The existence and uniqueness of solution is proved using a fixed point theorem. For the numerical solution of fractional model, we implemented a newly proposed Toufik-Atangana numerical scheme to validate the importance of arbitrary order derivative q and our obtained theoretical results. It is worth mentioning that fractional order derivative provides much deeper information about the complex dynamics of Corona model. Results obtained through the proposed scheme are dynamically consistent and good in agreement with the analytical results. To draw our conclusions, we explore a complete quantitative analysis of the given model for different quarantine levels. It is claimed through numerical simulations that pandemic could be eradicated faster if a human community selfishly adopts mandatory quarantine measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effectiveness of quarantine policy on human population. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
Citation - WoS: 2
Citation - Scopus: 2
On Wong Type Contractions
(Mdpi, 2020) Fulga, Andreea; Karapinar, Erdal
In this paper, by using admissible mapping, Wong type contraction mappings are extended and investigated in the framework of quasi-metric spaces to guarantee the existence of fixed points. We consider examples to illustrate the main results. We also demonstrate that the main results of the paper cover several existing results in the literature.
A Prelımınary Work On Investıgatıng Unıted Natıons’s Egovernment Crıterıa In Mıddle East Countrıes
(2017) Hussein, Mohammed; Pusatlı, O. Tolga
The benefits of e-government initiatives empowered by the information and communication technologies, are acknowledged widely with assessment criteria published by the United Nations regularly over the last 15 years. One of the reasons that United Nations has taken such assessment into agenda is the apparent advantages of such initiatives over the citizen, society and government. In parallel literature review and current status of Middle East countries, these issues are investigated with examples: Internet users, awareness and training, culture, intention to use e-government applications of the citizens, portal and interoperability. It is noted that assessment of human capital indices for these countries should be read carefully while considering these topics. The findings reveal the impact of human capital index on evaluating egovernment performance; geographical area and population also affect the adoption of e-government. For this, follow-up work is suggested to investigate the level of information and communication technology and computer literacy along with these factors in the region. This research has limitations which include the sources of information, exclusive economic and legal issues and a number of measurement methods.
Citation - WoS: 19
Citation - Scopus: 22
Generalized K-Mittag Function and Its Composition With Pathway Integral Operators
(int Scientific Research Publications, 2016) Purohit, S. D.; Abouzaid, M. S.; Al Qurashi, M.; Baleanu, D.; Nisar, K. S.
Our purpose in this paper is to consider a more generalized form of the Mittag-Leffler function. For this newly defined function, we obtain certain composition formulas with pathway fractional integral operators. We also point out some important special cases of the main results. (C) 2016 All rights reserved.
An Efficient Algorithm for the Numerical Evaluation of Pseudo Differential Operator With Error Estimation
(Amer inst Mathematical Sciences-aims, 2022) Pandey, Amit K.; Tripathi, Manoj P.; Singh, Harendra; Rao, Pentyala S.; Kumar, Devendra; Baleanu, D.
In this paper we introduce an efficient and new numerical algorithm for evaluating a pseudo differential operator. The proposed algorithm is time saving and fruitful. The theoretical as well as numerical error estimation of the algorithm is established, together with its stability analysis. We have provided numerical illustrations and established that the numerical findings echo the analytical findings. The proposed technique has a convergence rate of order three. CPU time of computation is also listed. Trueness of numerical findings are validated using figures.
Citation - WoS: 9
Citation - Scopus: 9
Positivity Preserving Computational Techniques for Nonlinear Autocatalytic Chemical Reaction Model
(Editura Acad Romane, 2020) Ahmed, Nauman; Baleanu, Dumitru; Baleanu, Dumitru; Korkmaz, Alper; Rafiq, Muhammad; Rehman, Muhammad Aziz-Ur; Ali, Mubasher; Matematik
In many physical problems, positivity is one of the most prevalent and imperative attribute of diverse mathematical models such as concentration of chemical reactions, population dynamics etc. However, the numerical discretization of dynamical systems that illustrate negative values may lead to meaningless solutions and sometimes to their divergence. The main objective of this work is to develop positivity preserving numerical schemes for the two-dimensional autocatalytic reaction diffusion Brusselator model. Two explicit finite difference (FD) schemes are proposed to solve numerically the two-dimensional Brusselator system. The proposed methods are the non-standard finite difference (NSFD) scheme and the unconditionally positivity preserving scheme. These numerical methods retain the positivity of the solution and the stability of the equilibrium point. Both proposed numerical schemes are compared with the forward Euler explicit FD scheme. The stability and consistency of all schemes are proved analytically and then verified by numerical simulations.
Citation - Scopus: 26
Search 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 Authors
Citation - WoS: 8
Citation - Scopus: 10
Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals
(Mdpi, 2019) Baleanu, Dumitru; Tchier, Fairouz; Purohit, Sunil Dutt; Mishra, Aditya Mani
An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.
Infectious Disease Dynamics within Advanced Fractional Operators
(2019) Defterli, Özlem; Arshad, Sadia; Jajarmi, Amin
Citation - WoS: 27
Citation - Scopus: 61
On the Approximate Solutions of Local Fractional Differential Equations With Local Fractional Operators
(Mdpi, 2016) Tchier, Fairouz; Baleanu, Dumitru; Jafari, Hossein; Jassim, Hassan Kamil
In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.
Citation - WoS: 4
Citation - Scopus: 2
A Fixed Point Theorem for Proinov Mappings With a Contractive Iterate
(Zhejiang Univ Press, 2023) Fulga, Andreea; Karapinar, Erdal
In this paper, we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point. In other words, we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces. We consider examples to illustrate the validity of the obtained result.
Citation - Scopus: 2
Non-Integer Variable Order Dynamic Equations on Time Scales Involving Caputo-Fabrizio Type Differential Operator
(Eudoxus Press, LLC, 2018) Baleanu, D.; Baleanu, Dumitru; Nategh, M.; Matematik
This work deals with the conecept of a Caputo-Fabrizio type non-integer variable order differential opertor on time scales that involves a non-singular kernel. A measure theoretic discussion on the limit cases for the order of differentiation is presented. Then, corresponding to the fractional derivative, we discuss on an integral for constant and variable orders. Beside the obtaining solutions to some dynamic problems on time scales involving the proposed derivative, a fractional folrmulation for the viscoelastic oscillation problem is studied and its conversion into a third order dynamic equation is presented. © 2018 by Eudoxus Press, LLC. All rights reserved.

Browse

Browsing Matematik Bölümü by Title