Matematik Bölümü Yayın Koleksiyonu

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

Browse

Now showing 1 - 10 of 10

A fractional model of convective radial fins with temperature-dependent thermal conductivity
(Editura Acad Romane, 2017) Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru
The principal purpose of the present article is to examine a fractional model of convective radial fins having constant and temperature-dependent thermal conductivity. In order to solve fractional order energy balance equation, a numerical algorithm namely homotopy analysis transform method is considered. The fin temperature is derived in terms of thermo-geometric fin parameter. Our method is not limited to the use of a small parameter, such as in the standard perturbation technique. The numerical simulation for temperature and fin tip temperature are presented graphically. The results can be used in thermal design to consider radial fins having both constant and temperature-dependent thermal conductivity.
A hybrid computational approach for Klein-Gordon equations on Cantor sets
(Springer, 2017) Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru
In this letter, we present a hybrid computational approach established on local fractional Sumudu transform method and homotopy perturbation technique to procure the solution of the Klein-Gordon equations on Cantor sets. Four examples are provided to show the accuracy and coherence of the proposed technique. The outcomes disclose that the present computational approach is very user friendly and efficient to compute the nondifferentiable solution of Klein-Gordon equation involving local fractional operator.
A novel numerical approach for a nonlinear fractional dynamical model of interpersonal and romantic relationships
(MDPI AG, 2017) Baleanu, Dumitru
In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian's decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter h and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems
(Sage Publications Ltd., 2017) Baleanu, Dumitru
The numerical solution of a fractional optimal control problem having a quadratic performance index is proposed and analyzed. The performance index of the fractional optimal control problem is considered as a function of both the state and the control variables. The dynamic constraint is expressed as a fractional differential equation that includes an integer derivative in addition to the fractional derivative. The order of the fractional derivative is taken as less than one and described in the Caputo sense. Based on the shifted Legendre orthonormal polynomials, we employ the operational matrix of fractional derivatives, the Legendre-Gauss quadrature formula and the Lagrange multiplier method for reducing such a problem into a problem consisting of solving a system of algebraic equations. The convergence of the proposed method is analyzed. For confirming the validity and accuracy of the proposed numerical method, a numerical example is presented along with a comparison between our numerical results and those obtained using the Legendre spectral-collocation method.
Anomalous diffusion models with general fractional derivatives within the kernels of the extended mittag-leffler type functions
(Editura Academiei Romane, 2017) Baleanu, Dumitru; Tenreiro Machado, J. A.; Baleanu, Dumitru
This paper addresses the new general fractional derivatives (GFDs) involving the kernels of the extended Mittag-Leffler type functions (MLFs). With the aid of the GFDs in the MLF kernels, the mathematical models for the anomalous diffusion of fractional order are analyzed and discussed. The proposed formulations are also used to describe complex phenomena that occur in heat transfer.
Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel
(INT Scientific Research Pub., 2017) Abdeljawad, Thabet; Baleanu, Dumitru
In this manuscript we define the right fractional derivative and its corresponding right fractional integral for the newly suggested nonlocal fractional derivative with Mittag-Leffler kernel. Then, we obtain the related integration by parts formula. We use the Q-operator to confirm our results. The related Euler-Lagrange equations are reported and one illustrative example is discussed.
New aspects of the adaptive synchronization and hyperchaos suppression of a financial model
(Pergamon-Elsevier Science, 2017) Baleanu, Dumitru; Hajipour, Mojtaba; Baleanu, Dumitru
This paper mainly focuses on the analysis of a hyperchaotic financial system as well as its chaos control and synchronization. The phase diagrams of the above system are plotted and its dynamical behaviours like equilibrium points, stability, hyperchaotic attractors and Lyapunov exponents are investigated. In order to control the hyperchaos, an efficient optimal controller based on the Pontryagin's maximum principle is designed and an adaptive controller established by the Lyapunov stability theory is also implemented. Furthermore, two identical financial models are globally synchronized by using an interesting adaptive control scheme. Finally, a fractional economic model is introduced which can also generate hyperchaotic attractors. In this case, a linear state feedback controller together with an active control technique are used in order to control the hyperchaos and realize the synchronization, respectively. Numerical simulations verifying the theoretical analysis are included.
New exact solutions of Burgers' type equations with conformable derivative
(Taylor&Francis Ltd., 2017) Baleanu, Dumitru; Baleanu, Dumitru; Kurt, Ali; Taşbozan, Orkun; 52063; 112385
In this paper, the new exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative. We use the first integral method to establish the exact solutions for time-fractional Burgers' equation, modified Burgers' equation, and Burgers-Korteweg-de Vries equation. We report that this method is efficient and it can be successfully used to obtain new analytical solutions of nonlinear FDEs.
Relaxation and diffusion models with non-singular kernels
(Elsevier Science Bv., 2017) Baleanu, Dumitru
Anomalous relaxation and diffusion processes have been widely quantified by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to its limitation in describing different kinds of non-exponential decays (e.g. stretched exponential decay). Meanwhile, many efforts by mathematicians and engineers have been made to overcome the singularity of power function kernel in its definition. This study first explores physical properties, of relaxation and diffusion models where the temporal derivative was defined recently using an exponential kernel. Analytical analysis shows that the Caputo type derivative model with an exponential kernel cannot characterize non-exponential dynamics well-documented in anomalous relaxation and diffusion. A legitimate extension of the previous derivative is then proposed by replacing the exponential kernel with a stretched" exponential kernel. Numerical tests show that the Caputo type derivative model with the stretched exponential kernel can describe a much wider range of anomalous diffusion than the exponential kernel, implying the potential applicability of the new derivative in quantifying real-world, anomalous relaxation and diffusion processes.
Stability analysis of Caputo-like discrete fractional systems
(Elsevier Science Bv., 2017) Baleanu, Dumitru
This study investigates stability of Caputo delta fractional difference equations. Solutions' monotonicity and asymptotic stability of a linear fractional difference equation are discussed. A stability theorem for a discrete fractional Lyapunov direct method is proved. Furthermore, an inequality is extended from the continuous case and a sufficient condition is given. Some linear, nonlinear and time varying examples are illustrated and the results show wide prospects of the stability theorems in fractional control systems of discrete time.

Browse

Browsing Matematik Bölümü Yayın Koleksiyonu by Department "Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bilgisayar Bölümü"