Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
20 results
Search Results
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: 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: 25Citation - Scopus: 37A Solution of the Fractional Differential Equations in the Setting of B-Metric Space(Vasyl Stefanyk Precarpathian Natl Univ, 2021) Afshari, H.; Karapinar, E.In this paper, we study the existence of solutions for the following differential equations by using a fixed point theorems {D(c)(mu)w(sigma) +/- D(c)(nu)w(sigma) = h(sigma, w(sigma)), sigma is an element of J, 0 < nu < mu < 1, w(0) = w(0), where D-mu, D-nu is the Caputo derivative of order mu, nu, respectively and h: J x R -> R is continuous. The results are well demonstrated with the aid of exciting examples.Article Citation - WoS: 4Citation - Scopus: 5A New Analytical Method To Simulate the Mutual Impact of Space-Time Memory Indices Embedded in (1(de Gruyter Poland Sp Z O O, 2022) Jaradat, Imad; Alquran, Marwan; Baleanu, Dumitru; Makhadmih, MohammadIn the present article, we geometrically and analytically examine the mutual impact of space-time Caputo derivatives embedded in (1 + 2)-physical models. This has been accomplished by integrating the residual power series method (RPSM) with a new trivariate fractional power series representation that encompasses spatial and temporal Caputo derivative parameters. Theoretically, some results regarding the convergence and the error for the proposed adaptation have been established by virtue of the Riemann-Liouville fractional integral. Practically, the embedding of Schrodinger, telegraph, and Burgers' equations into higher fractional space has been considered, and their solutions furnished by means of a rapidly convergent series that has ultimately a closed-form fractional function. The graphical analysis of the obtained solutions has shown that the solutions possess a homotopy mapping characteristic, in a topological sense, to reach the integer case solution where the Caputo derivative parameters behave similarly to the homotopy parameters. Altogether, the proposed technique exhibits a high accuracy and high rate of convergence.Article Citation - WoS: 13Citation - Scopus: 16A Robust Scheme for Caputo Variable-Order Time-Fractional Diffusion-Type Equations(Springer, 2023) Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Hincal, Evren; Sadri, KhadijehThe focus of this work is to construct a pseudo-operational Jacobi collocation scheme for numerically solving the Caputo variable-order time-fractional diffusion-type equations with applications in applied sciences. Modeling scientific phenomena in the context of fluid flow problems, curing reactions of thermosetting systems, solid oxide fuel cells, and solvent diffusion into heavy oils led to the appearance of these equations. For this reason, the numerical solution of these equations has attracted a lot of attention. More precisely, using pseudo-operational matrices and appropriate approximations based on bivariate Jacobi polynomials, the approximate solutions of the variable-order time-fractional diffusion-type equations in the Caputo sense with high accuracy are formally retrieved. Based on orthogonal bivariate Jacobi polynomials and their operational matrices, a sparse algebraic system is generated which makes implementing the proposed approach easy. An error bound is computed for the residual function by proving some theorems. To illustrate the accuracy and efficiency of the scheme, several illustrative examples are considered. The results demonstrate the efficiency of the present method compared to those achieved by the Legendre and Lucas multi-wavelet methods and the Crank-Nicolson compact method.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 - Scopus: 22Solitary Wave Solution for a Generalized Hirota-Satsuma Coupled Kdv and Mkdv Equations: a Semi-Analytical Approach(Elsevier B.V., 2020) Chakraverty, S.; Baleanu, D.; Jena, R.M.Nonlinear fractional differential equations (NFDEs) offer an effective model of numerous phenomena in applied sciences such as ocean engineering, fluid mechanics, quantum mechanics, plasma physics, nonlinear optics. Some studies in control theory, biology, economy, and electrodynamics, etc. demonstrate that NFDEs play the primary role in explaining various phenomena arising in real-life. Now-a-day NFDEs in various scientific fields in particular optical fibers, chemical physics, solid-state physics, and so forth have the most important subjects for study. Finding exact responses to these equations will help us to a better understanding of our environmental nonlinear physical phenomena. In this regard, in the present study, we have applied fractional reduced differential transform method (FRDTM) to obtain the solution of nonlinear time-fractional Hirota-Satsuma coupled KdV and MKdV equations. The novelty of the FRDTM is that it does not require any discretization, transformation, perturbation, or any restrictive conditions. Moreover, this method requires less computation compared to other methods. Computed results are compared with the existing results for the special cases of integer order. The present results are in good agreement with the existing solutions. Here, the fractional derivatives are considered in the Caputo sense. The presented method is a semi-analytical method based on the generalized Taylor series expansion and yields an analytical solution in the form of a polynomial. © 2020 Faculty of Engineering, Alexandria UniversityArticle 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: 37Citation - Scopus: 45An Effective Computational Method To Deal With a Time-Fractional Nonlinear Water Wave Equation in the Caputo Sense(Elsevier, 2021) Ilie, Mousa; Mirzazadeh, Mohammad; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadir; Baleanu, Dumitru; Salahshour, Soheil; Hosseini, KamyarThe authors' concern of the present paper is to conduct a systematic study on a time-fractional nonlinear water wave equation which is an evolutionary version of the Boussinesq system. The study goes on by adopting a new analytical method based on the Laplace transform and the homotopy analysis method to the governing model and obtaining its approximate solutions in the presence of the Caputo fractional derivative. To analyze the influence of the Caputo operator on the dynamical behavior of the approximate solutions, some graphical illustrations in two- and three-dimensions are formally presented. Furthermore, several numerical tables are given to support the performance of the new analytical method in handling the time-fractional nonlinear water wave equation. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.