Fen - Edebiyat Fakültesi
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Browsing Fen - Edebiyat Fakültesi by Department "Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü"
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Article A hybrid stochastic fractional order Coronavirus (2019-nCov) mathematical model(2021) Baleanu, Dumitru; Al-Mekhlafi, S. M.; Baleanu, Dumitru; 56389; MatematikIn this paper, a new stochastic fractional Coronavirus (2019-nCov) model with modified parameters is presented. The proposed stochastic COVID-19 model describes well the real data of daily confirmed cases in Wuhan. Moreover, a novel fractional order operator is introduced, it is a linear combination of Caputo's fractional derivative and Riemann-Liouville integral. Milstein's higher order method is constructed with the new fractional order operator to study the model problem. The mean square stability of Milstein algorithm is proved. Numerical results and comparative studies are introduced.Article A k-Dimensional System of Fractional Finite Difference Equations(2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; 56389; MatematikWe investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.Article A new algorithm for solving dynamic equations on a time scale(2017) Baleanu, Dumitru; Haghbin, A.; Johnston, S. J.; Baleanu, Dumitru; 56389; MatematikIn this paper, we propose a numerical algorithm to solve a class of dynamic time scale equation which is called the q-difference equation. First, we apply the method for solving initial value problems (IVPs) which contain the first and second order delta derivatives. Illustrative examples show the usefulness of the method. Then we present applications of the method for solving the strongly non-linear damped q-difference equation. The results show that our method is more accurate than the other existing method. (C) 2016 Elsevier B.V. All rights reserved.Article A New Class of Contraction in b -Metric Spaces and Applications(2017) Kaushik, P.; Kumar, S.; Kenan, Taş; 4971A novel class of α-β-contraction for a pair of mappings is introduced in the setting of b-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation. © 2017 Preeti Kaushik et al.Article A note on (p, q)-analogue type of Fubini numbers and polynomials(2020) Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389; MatematikIn this paper, we introduce a new class of (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for (p, q)-Fubini polynomials associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials and (p, q)-Stirling numbers of the second kind.p>
Article About fractional quantization and fractional variational principles(2009) Baleanu, Dumitru; 56389; Matematikin this paper, a new method of finding the fractional Euler-Lagrange equations within Caputo derivative is proposed by making use of the fractional generalization of the classical Fad di Bruno formula. The fractional Euler-Lagrange and the fractional Hamilton equations are obtained within the 1 + 1 field formalism. One illustrative example is analyzed. (C) 2008 Elsevier B.V. All rights reserved.Article Accurate novel explicit complex wave solutions of the (2+1)-dimensional Chiral nonlinear Schrodinger equation(2021) Baleanu, Dumitru; Yakout, H. A.; Khater, Mostafa M. A.; Abdel-Aty, Abdel-Haleem; Mahmoud, Emad E.; Baleanu, Dumitru; Eleuch, Hichem; 56389; MatematikThis manuscript investigates the accuracy of the solitary wave solutions of the (2+1)-dimensional nonlinear Chiral Schrodinger ((2+1)-D CNLS) equation that are constructed by employing two recent analytical techniques (modified Khater (MKhat) and modified Jacobian expansion (MJE) methods). This investigation is based on evaluating the initial and boundary conditions through the obtained analytical solutions then employing the Adomian decomposition (AD) method to evaluate the approximate solutions of the (2+1)-D CNLS equation. This framework gives the ability to get large complex traveling wave solutions of the considered model and shows the superiority of the employed computational schemes by comparing the absolute error for each of them. The handled model describes the edge states of the fractional quantum hall effect. Many novel solutions are obtained with various formulas such as trigonometric, rational, and hyperbolic to the studied model. For more illustration of the results, some solutions are displayed in 2D, 3D, and density plots.Article AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE(2019) Baleanu, Dumitru; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa; 56389; MatematikIn this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.Article An Analytical Study of (2+1)-Dimensional Physical Models Embedded Entirely in Fractal Space(Editura Academiei Romane, 2019) Baleanu, Dumitru; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa; 56389; MatematikIn this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.Article AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE(2019) Baleanu, Dumitru; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa; 56389; MatematikIn this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.Article An e ffective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator(2023) Baleanu, Dumitru; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; 56389; MatematikIn this paper, under some conditions in the Banach space C([0; beta];R), we establish the existence and uniqueness of the solution for the nonlinear integral equations involving the Riemann-Liouville fractional operator (RLFO). To establish the requirements for the existence and uniqueness of solutions, we apply the Leray-Schauder alternative and Banach's fixed point theorem. We analyze Hyers-Ulam-Rassias (H-U-R) and Hyers-Ulam (H-U) stability for the considered integral equations involving the RLFO in the space C([0; beta];R). Also, we propose an e ffective and e fficient computational method based on Laguerre polynomials to get the approximate numerical solutions of integral equations involving the RLFO. Five examples are given to interpret the method.Article An exact analytical solution of the unsteady magnetohydrodynamics nonlinear dynamics of laminar boundary layer due to an impulsively linear stretching sheet(2017) Baleanu, Dumitru; Nagaraju, K. R.; Kumar, P. N. Vinay; Baleanu, Dumitru; Lorenzini, Giulio; 56389; MatematikIn this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.Article Analysis of the family of integral equation involving incomplete types of I and Ī-functions(2023) Baleanu, Dumitru; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil Dutt; 56389; MatematikThe present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.Article Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations(2017) Baleanu, Dumitru; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas; 56389; MatematikIn this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.Article Asymptotic Integration of (1+Alpha)-Order Fractional Differential Equations(Pergamon-Elsevier Science LTD, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389; MatematikWe establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0. (C) 2011 Elsevier Ltd. All rights reserved.Book Part Calculus on Fractals(De Gruyter, 2015) Baleanu, Dumitru; Baleanu, Dumitru; 56389; MatematikIn this chapter we present a framework and a calculus on fractals. The sug-gested equation has been solved and applied in physics and dynamics.Book Part Calculus on fractals(2015) Baleanu, Dumitru; Baleanu, Dumitru; 56389; MatematikIn this chapter we present a framework and a calculus on fractals. The suggested equation has been solved and applied in physics and dynamics.Article Cantor-type spherical-coordinate Method for Differential Equations within Local Fractional Derivatives(2015) Baleanu, Dumitru; Baleanu, Dumitru; Yang, Xiao-Jun; 56389; MatematikIn this article, we utilize the Cantor-type spherical coordinate method to investigate a family of local fractional differential operators on Cantor sets. Some examples are discussed to show the capability of this method for the damped wave, Helmholtz and heat conduction equations defined on Cantor sets. We show that it is a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type spherical-coordinate systems.Article Chain and Hamilton-Jacobi approaches for systems with purely second class constraints(2003) Baleanu, Dumitru; Güler, Y.; 56389; MatematikThe equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.Article Comparative study for optimal control nonlinear variable -order fractional tumor model(2020) Baleanu, Dumitru; AL-Mekhlafi, S. M; Alshomrani, A. S.; Baleanu, Dumitru; 56389; MatematikThis article presents a variable order nonlinear mathematical model and its optimal control for a Tumor under immune suppression. The formulation generalizes the one proposed by Kim et. al. consisting of eleven integer order differential equations. The new approach adopts a variable-order fractional model with the derivatives defined in the Caputo sense. Two control variables, one for immunotherapy and one for Chemotherapy, are proposed to eliminate or reduce the Tumor cells. A simple numerical technique called the nonstandard generalized Euler method is developed to solve the proposed optimal control problem. Moreover, the stability analysis and the truncation error are studied. Numerical simulations and comparative studies are implemented. Our findings disclose that the proposed scheme used here has two main advantages: it is faster than the generalized Euler scheme and it can reduce the number of Tumor cells in a proper process better than the second scheme.
