Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Citation - WoS: 4
Citation - Scopus: 3
2D gravity and the Hamilton-Jacobi formalism
(Soc Italiana Fisica, 2002) Baleanu, D; Baleanu, Dumitru; Güler, Y; 56389; Matematik
Hamilton-Jacobi formalism is used to study 2D gravity and its SL(2, R) hidden symmetry. If the contribution of the surface term is considered, the obtained results coincide with those given by the Dirac and Faddeev-Jackiw approaches.
Citation - WoS: 7
Citation - Scopus: 5
A Brief Overview and Survey of the Scientific Work by Feng Qi
(Mdpi, 2022) Agarwal, Ravi Prakash; Karapinar, Erdal; Kostic, Marko; Cao, Jian; Du, Wei-Shih; 19184
In the paper, the authors present a brief overview and survey of the scientific work by Chinese mathematician Feng Qi and his coauthors.
Citation - WoS: 72
Citation - Scopus: 99
A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel
(Springer, 2018) Baleanu, D.; Baleanu, Dumitru; Shiri, B.; Srivastava, H. M.; Al Qurashi, M.; 56389; Matematik
In this paper, we solve a system of fractional differential equations within a fractional derivative involving the Mittag-Leffler kernel by using the spectral methods. We apply the Chebyshev polynomials as a base and obtain the necessary operational matrix of fractional integral using the Clenshaw-Curtis formula. By applying the operational matrix, we obtain a system of linear algebraic equations. The approximate solution is computed by solving this system. The regularity of the solution investigated and a convergence analysis is provided. Numerical examples are provided to show the effectiveness and efficiency of the method.
Citation - WoS: 20
Citation - Scopus: 24
A coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives
(Springer, 2020) Baleanu, D.; Baleanu, Dumitru; Alzabut, J.; Jonnalagadda, J. M.; Adjabi, Y.; Matar, M. M.; 56389; Matematik
In this paper, we study a coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations described by Atangana-Baleanu-Caputo (ABC for short) derivatives whose formulations are based on the notable Mittag-Leffler kernel. Prior to the main results, the equivalence of the coupled system to a nonlinear system of integral equations is proved. Once that has been done, we show in detail the existence-uniqueness and Ulam stability by the aid of fixed point theorems. Further, the continuous dependence of the solutions is extensively discussed. Some examples are given to illustrate the obtained results.
Citation - WoS: 8
Citation - Scopus: 12
A detailed study on a new (2+1)-dimensional mKdV equation involving the Caputo-Fabrizio time-fractional derivative
(Springer, 2020) Hosseini, K.; Baleanu, Dumitru; Ilie, M.; Mirzazadeh, M.; Baleanu, D.; 56389; Matematik
The present article aims to present a comprehensive study on a nonlinear time-fractional model involving the Caputo-Fabrizio (CF) derivative. More explicitly, a new (2+1)-dimensional mKdV (2D-mKdV) equation involving the Caputo-Fabrizio time-fractional derivative is considered and an analytic approximation for it is retrieved through a systematic technique, called the homotopy analysis transform (HAT) method. Furthermore, after proving the Lipschitz condition for the kernel psi (x,y,t;u), the fixed-point theorem is formally utilized to demonstrate the existence and uniqueness of the solution of the new 2D-mKdV equation involving the CF time-fractional derivative. A detailed study finally is carried out to examine the effect of the Caputo-Fabrizio operator on the dynamics of the obtained analytic approximation.
Citation - WoS: 19
Citation - Scopus: 22
A discussion on a generalized Geraghty multi-valued mappings and applications
(Springer, 2020) Afshari, Hojjat; Karapınar, Erdal; Atapour, Maryam; Karapinar, Erdal; 19184; Matematik
This research intends to investigate the existence results for both coincidence points and common fixed point of generalized Geraghty multi-valued mappings endowed with a directed graph. The proven results are supported by an example. We also consider fractional integral equations as an application.
Citation - WoS: 9
Citation - Scopus: 10
A Discussion On the Existence of Best Proximity Points That Belong to the Zero Set
(Mdpi, 2020) Karapinar, Erdal; Karapınar, Erdal; Abbas, Mujahid; Farooq, Sadia; 19184; Matematik
In this paper, we investigate the existence of best proximity points that belong to the zero set for the alpha p -admissible weak (F,phi) -proximal contraction in the setting of M-metric spaces. For this purpose, we establish phi -best proximity point results for such mappings in the setting of a complete M-metric space. Some examples are also presented to support the concepts and results proved herein. Our results extend, improve and generalize several comparable results on the topic in the related literature.
Citation - Scopus: 105
A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces
(Springer Science and Business Media Deutschland GmbH, 2020) Afshari, H.; Karapınar, Erdal; Karapınar, E.; 19184; Matematik
In this paper, we investigate the existence of positive solutions for the new class of boundary value problems via ψ-Hilfer fractional differential equations. For our purpose, we use the α− ψ Geraghty-type contraction in the framework of the b-metric space. We give an example illustrating the validity of the proved results. © 2020, The Author(s).
Citation - WoS: 1
Citation - Scopus: 1
A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes
(Springer, 2021) Hameed, Rabia; Baleanu, Dumitru; Mustafa, Ghulam; Baleanu, Dumitru; Chu, Yu-Ming; 56389; Matematik
In this article, we present the continuity analysis of the 3D models produced by the tensor product scheme of (m + 1)-point binary refinement scheme. We use differences and divided differences of the bivariate refinement scheme to analyze its smoothness. The C-0, C(1 )and C-2 continuity of the general bivariate scheme is analyzed in our approach. This gives us some simple conditions in the form of arithmetic expressions and inequalities. These conditions require the mask and the complexity of the given refinement scheme to analyze its smoothness. Moreover, we perform several experiments by using these conditions on established schemes to verify the correctness of our approach. These experiments show that our results are easy to implement and are applicable for both interpolatory and approximating types of the schemes.
Citation - WoS: 5
Citation - Scopus: 5
A Filter Method for Inverse Nonlinear Sideways Heat Equation
(Springer, 2020) Nguyen Anh Triet; Baleanu, Dumitru; O'Regan, Donal; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Can; 56389; Matematik
In this paper, we study a sideways heat equation with a nonlinear source in a bounded domain, in which the Cauchy data at x=X are given and the solution in 0 <= x < X is sought. The problem is severely ill-posed in the sense of Hadamard. Based on the fundamental solution to the sideways heat equation, we propose to solve this problem by the filter method of degree alpha, which generates a well-posed integral equation. Moreover, we show that its solution converges to the exact solution uniformly and strongly in L-p(omega,X; L-2 (R)); omega is an element of[0,X) under a priori assumptions on the exact solution. The proposed regularized method is illustrated by numerical results in the final section.
Citation - WoS: 44
Citation - Scopus: 51
A finite difference scheme based on cubic trigonometric B-splines for a time fractional diffusion-wave equation
(Springeropen, 2017) Yaseen, Muhammad; Baleanu, Dumitru; Abbas, Muhammad; Nazir, Tahir; Baleanu, Dumitru; 56389; Matematik
In this paper, we propose an efficient numerical scheme for the approximate solution of a time fractional diffusion-wave equation with reaction term based on cubic trigonometric basis functions. The time fractional derivative is approximated by the usual finite difference formulation, and the derivative in space is discretized using cubic trigonometric B-spline functions. A stability analysis of the scheme is conducted to confirm that the scheme does not amplify errors. Computational experiments are also performed to further establish the accuracy and validity of the proposed scheme. The results obtained are compared with finite difference schemes based on the Hermite formula and radial basis functions. It is found that our numerical approach performs superior to the existing methods due to its simple implementation, straightforward interpolation and very low computational cost. A convergence analysis of the scheme is also discussed.
Citation - WoS: 6
A fite type result for sequental fractional differintial equations
(Dynamic Publishers, inc, 2010) Abdeljawad, Thabet; Abdeljawad, T.; Baleanu, Dumitru; Baleanu, D.; Jarad, Fahd; Jarad, Fahd; Mustafa, O. G.; Trujillo, J. J.; Matematik
Given the solution f of the sequential fractional differential equation aD(t)(alpha)(aD(t)(alpha) f) + P(t)f = 0, t is an element of [b, a], where -infinity < a < b < c < + infinity, alpha is an element of (1/2, 1) and P : [a, + infinity) -> [0, P-infinity], P-infinity < + infinity, is continuous. Assume that there exist t(1),t(2) is an element of [b, c] such that f(t(1)) = (aD(t)(alpha))(t(2)) = 0. Then, we establish here a positive lower bound for c - a which depends solely on alpha, P-infinity. Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations.
Citation - WoS: 18
Citation - Scopus: 22
A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations
(Springer, 2019) Amin, Muhammad; Baleanu, Dumitru; Abbas, Muhammad; Iqbal, Muhammad Kashif; Ismail, Ahmad Izani Md.; Baleanu, Dumitru; 56389; Matematik
The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivative, while non-polynomial quintic spline is employed as an interpolating function in the spatial direction. The proposed method is shown to be unconditionally stable and O(h(4) + Delta t(2)) accurate. In order to check the feasibility of the proposed technique, some test examples have been considered and the simulation results are compared with those available in the existing literature.
Citation - WoS: 37
Citation - Scopus: 63
A fractional derivative with two singular kernels and application to a heat conduction problem
(Springer, 2020) Baleanu, Dumitru; Baleanu, Dumitru; Jleli, Mohamed; Kumar, Sunil; Samet, Bessem; 56389; Matematik
In this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established and some examples are provided. We also present some applications to fractional differential equations and propose a numerical algorithm based on a Picard iteration for approximating the solutions. Finally, an application to a heat conduction problem is given.
Citation - WoS: 152
Citation - Scopus: 184
A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative
(Springer, 2020) Baleanu, Dumitru; Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389; Matematik
We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.
Citation - Scopus: 1
A Fractional Lagrangian Approach for Two Masses with Linear and Cubic Nonlinear Stiffness
(Institute of Electrical and Electronics Engineers Inc., 2023) Defterli, O.; Defterli, Özlem; Baleanu, D.; Jajarmi, A.; Wannan, R.; Asad, J.; 31401; 56389; Matematik
In this manuscript, the fractional dynamics of the two-mass spring system with two kinds of stiffness, namely linear and strongly nonlinear, are investigated. The corresponding fractional Euler-Lagrange equations of the system are derived being a system of two-coupled fractional differential equations with strong cubic nonlinear term. The numerical results of the system are obtained using Euler's approximation method and simulated with respect to the different values of the model parameters as mass, stiffness and order of the fractional derivative in use. The interpretation of the approximate results of the so-called generalized two-mass spring system is discussed via the fractional order. © 2023 IEEE.
Citation - Scopus: 0
A General Form of Fractional Derivatives for Modelling Purposes in Practice
(Institute of Electrical and Electronics Engineers Inc., 2023) Jajarmi, A.; Baleanu, Dumitru; Baleanu, D.; 56389; Matematik
In this paper, we propose new mathematical models for the complex dynamics of the world population growth as well as a human body's blood ethanol concentration by using a general formulation in fractional calculus. In these new models, we employ a recently introduced ψ-Caputo fractional derivative whose kernel is defined based on another function. Meanwhile, a number of comparative experiences are carried out in order to verify the models according to some sets of real data. Simulation results indicate that better approximations are achieved when the systems are modeled by using the new general fractional formulation than the other cases of fractional- and integer-order descriptions. © 2023 IEEE.
Citation - WoS: 16
A general treatment of singular Lagrangians with linear velocities
(Editrice Compositori Bologna, 2000) Baleanu, D; Baleanu, Dumitru; Güler, Y; 56389; Matematik
The Hamilton-Jacobi treatment of singular systems with linear velocities is investigated. Since the rank of Hessian matrix is zero, all the generalized coordinates are independent parameters. Integrability conditions reduce the degrees of freedom. Path integral quantization is analyzed.
Citation - WoS: 67
Citation - Scopus: 88
A generalized Lyapunov-type inequality in the frame of conformable derivatives
(Springeropen, 2017) Abdeljawad, Thabet; Abdeljawad, Thabet; Alzabut, Jehad; Alzabut, Jehad; Jarad, Fahd; Jarad, Fahd; 234808; Matematik
We prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order alpha is an element of (1, 2]. Indeed, it is shown that if the boundary value problem (T(alpha)(c)x)(t) + r(t) x(t) = 0, t is an element of (c, d), x(c) = x(d) = 0 has a nontrivial solution, where r is a real-valued continuous function on [c, d], then integral(d)(c) vertical bar r(t)vertical bar dt > alpha(alpha)/(alpha - 1)(alpha-1) (d - c)(a-1). (1) Moreover, a Lyapunov type inequality of the form integral(d)(c)vertical bar r(t)vertical bar dt > 3 alpha - 1/(d - c)(2 alpha-1) (3 alpha - 1/2 alpha - 1)(2 alpha-1/a), 1/2 < alpha <= 1, (2) is obtained for a sequential conformable BVP. Some examples are given and an application to conformable Sturm-Liouville eigenvalue problem is analyzed.
Citation - WoS: 12
Citation - Scopus: 14
A generalized study of the distribution of buffer over calcium on a fractional dimension
(Taylor & Francis Ltd, 2023) Bhatter, Sanjay; Baleanu, Dumitru; Jangid, Kamlesh; Kumawat, Shyamsunder; Purohit, Sunil Dutt; Baleanu, Dumitru; Suthar, D. L.; 56389; Matematik
Calcium is an essential element in our body and plays a vital role in moderating calcium signalling. Calcium is also called the second messenger. Calcium signalling depends on cytosolic calcium concentration. In this study, we focus on cellular calcium fluctuations with different buffers, including calcium-binding buffers, using the Hilfer fractional advection-diffusion equation for cellular calcium. Limits and start conditions are also set. By combining with intracellular free calcium ions, buffers reduce the cytosolic calcium concentration. The buffer depletes cellular calcium and protects against toxicity. Association, dissociation, diffusion, and buffer concentration are modelled. The solution of the Hilfer fractional calcium model is achieved through utilizing the integral transform technique. To investigate the influence of the buffer on the calcium concentration distribution, simulations are done in MATLAB 21. The results show that the modified calcium model is a function of time, position, and the Hilfer fractional derivative. Thus the modified Hilfer calcium model provides a richer physical explanation than the classical calcium model.

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