WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
Browse
30 results
Search Results
Article Citation - WoS: 3Citation - Scopus: 4Numerical Analysis of Fractional Order Discrete Bloch Equa-Tions(int Scientific Research Publications, 2024) Santra, Shyam Sundar; Jayanathan, Leo Amalraj; Baleanu, Dumitru; Murugesan, MeganathanBy defining a new kind of h-extorial function with constant coefficient, this research seeks to solve discrete fractional Bloch equations. By using an extorial function of the Mittag-Leffler type, we are able to discover the general solutions for the magnetization's Bx, By, and Bz components. These findings demonstrate the innovative method of fractional order Bloch equations. In addition, we offer a graphical representation of our results.(c) 2024 All rights reserved.Article Citation - WoS: 16Citation - Scopus: 15Fractional Hyper-Chaotic System With Complex Dynamics and High Sensitivity: Applications in Engineering(World Scientific Publ Co Pte Ltd, 2024) Yusuf, Abdullahi; Alshomrani, Ali S. S.; Sulaiman, Tukur Abdulkadir; Baleanu, Dumitru; Partohaghighi, MohammadHyper-chaotic systems have useful applications in engineering applications due to their complex dynamics and high sensitivity. This research is supposed to introduce and analyze a new noninteger hyper-chaotic system. To design its fractional model, we consider the Caputo fractional operator. To obtain the approximate solutions of the extracted system under the considered fractional-order derivative, we employ an accurate nonstandard finite difference (NSFD) algorithm. Moreover, the existence and uniqueness of the solutions are provided using the theory of fixed-point. Also, to see the performance of the utilized numerical scheme, we choose different values of fractional orders along with various amounts of the initial conditions (ICs). Graphs of solutions for each case are provided.Article Citation - WoS: 41Citation - Scopus: 44Nonlinear Dynamics and Chaos in Fractional Differential Equations With a New Generalized Caputo Fractional Derivative(Elsevier, 2022) Baleanu, Dumitru; Odibat, ZaidIn this paper, novel systems of fractional differential equations involving a new generalized Caputo fractional derivative were proposed. The complex dynamic behavior of these systems was studied by numerical simulation. Nonlinear dynamics and chaos in hybrid fractional order systems were investigated using a predictor-corrector algorithm. In particular, the effect of the new generalized fractional derivative parameters on the dynamics of the proposed systems was discussed. The rich variation obtained from the characteristics of the studied systems recommends the implementation of the new generalized derivative in fractional calculus applications.Article Citation - WoS: 2Citation - Scopus: 2Fractional Evolution Equation With Cauchy Data in L<sup>p</Sup> Spaces(Springer, 2022) Baleanu, Dumitru; Agarwal, Ravi P.; Le Dinh Long; Nguyen Duc Phuong; Long, Le Dinh; Phuong, Nguyen DucIn this paper, we consider the Cauchy problem for fractional evolution equations with the Caputo derivative. This problem is not well posed in the sense of Hadamard. There have been many results on this problem when data is noisy in L-2 and H-s,H- However, there have not been any papers dealing with this problem with observed data in L-p with p not equal 2. We study three cases of source functions: homogeneous case, inhomogeneous case, and nonlinear case. For all of them, we use a truncation method to give an approximate solution to the problem. Under different assumptions on the smoothness of the exact solution, we get error estimates between the regularized solution and the exact solution in L-p. To our knowledge, L-p evaluations for the inverse problem are very limited. This work generalizes some recent results on this problem.Article Citation - WoS: 4Citation - Scopus: 4Continuity Result on the Order of a Nonlinear Fractional Pseudo-Parabolic Equation With Caputo Derivative(Mdpi, 2021) Hoang, Luc Nguyen; Baleanu, Dumitru; Van, Ho Thi Kim; Binh, Ho DuyIn this paper, we consider a problem of continuity fractional-order for pseudo-parabolic equations with the fractional derivative of Caputo. Here, we investigate the stability of the problem with respect to derivative parameters and initial data. We also show that u(omega ') -> u(omega) in an appropriate sense as omega '-> omega, where omega is the fractional order. Moreover, to test the continuity fractional-order, we present several numerical examples to illustrate this property.Article Citation - WoS: 29Citation - Scopus: 33A New Fractional Derivative Operator With Generalized Cardinal Sine Kernel: Numerical Simulation(Elsevier, 2023) Baleanu, Dumitru; Odibat, ZaidIn this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann-Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.Article Citation - WoS: 68Citation - Scopus: 74On Continuity of the Fractional Derivative of the Time-Fractional Semilinear Pseudo-Parabolic Systems(Springer, 2021) Ho Duy Binh; Nguyen Hoang Luc; Nguyen Huu Can; Karapinar, Erdal; Binh, Ho Duy; Luc, Nguyen Hoang; Can, Nguyen HuuIn this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order derivative. To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by constants independent of the derivative order. Moreover, we present an example to illustrate the theory.Article Citation - WoS: 25Citation - Scopus: 22Numerical Approximation of Inhomogeneous Time Fractional Burgers-Huxley Equation With B-Spline Functions and Caputo Derivative(Springer, 2022) Kamran, Mohsin; Asghar, Noreen; Baleanu, Dumitru; Majeed, AbdulA prototype model used to explain the relationship between mechanisms of reaction, convection effects, and transportation of diffusion is the generalized Burgers-Huxley equation. This study presents numerical solution of non-linear inhomogeneous time fractional Burgers-Huxley equation using cubic B-spline collocation method. For this purpose, Caputo derivative is used for the temporal derivative which is discretized by L1 formula and spatial derivative is interpolated with the help of B-spline basis functions, so the dependent variable is continuous throughout the solution range. The validity of the proposed scheme is examined by solving four test problems with different initial-boundary conditions. The algorithm for the execution of scheme is also presented. The effect of non-integer parameter alpha and time on dependent variable is studied. Moreover, convergence and stability of the proposed scheme is analyzed, and proved that scheme is unconditionally stable. The accuracy is checked by error norms. Based on obtained results we can say that the proposed scheme is a good addition to the existing schemes for such real-life problems.Article Citation - WoS: 75Citation - Scopus: 82Mathematical Modeling of Pine Wilt Disease With Caputo Fractional Operator(Pergamon-elsevier Science Ltd, 2021) Acay, Bahar; Mustapha, Umar Tasiu; Inc, Mustafa; Baleanu, Dumitru; Yusuf, AbdullahiIn this work, we investigate the transmission dynamics of pine wilt disease infection and developed a new model utilizing Caputo fractional-order derivative. Moreover, with the use of fixed point theorem, the existence and uniqueness of the pine wilt disease model are obtained under Caputo operator. Using forward normalized sensitivity index, we determine the most sensitive parameters essential for the control of the infection and the results show that, decreasing the values of contact rate of a susceptible vector with infected pine trees and progression rate play a significant role in controlling the spread of pine wilt disease infection. On the other hand, we obtain different numerical simulations results of the model using the appropriate parameter values. Hence, from the graphs, it can be concluded that Caputo fractional operator gives more biologically observable behavior of the proposed disease model thanks to the changed fractional order. Compared to the previously built integer order model, the non-integer order derivative provided more efficient and flexible information about the complexity of the model's dynamics. (c) 2020 Elsevier Ltd. All rights reserved.Article Citation - WoS: 16Citation - Scopus: 19Finite-Time Stability of Linear Stochastic Fractional-Order Systems With Time Delay(Springer, 2021) Ben Makhlouf, Abdellatif; Baleanu, Dumitru; Rhaima, Mohamed; Mchiri, LassaadThis paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for alpha is an element of (1/2, 1). Under the generalized Gronwall inequality and stochastic analysis techniques, the finite-time stability of the solution for linear stochastic fractional-order systems with time delay is investigated. We give two illustrative examples to show the interest of the main results.
- «
- 1 (current)
- 2
- 3
- »