University of Tabriz

About: University of Tabriz is a education organization based out in Tabriz, Iran. It is known for research contribution in the topics: Population & Nanocomposite. The organization has 12141 authors who have published 20976 publications receiving 313982 citations.

A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel

Abstract: 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.

Collocation methods for fractional differential equations involving non-singular kernel

Abstract: A system of fractional differential equations involving non-singular Mittag-Leffler kernel is considered. This system is transformed to a type of weakly singular integral equations in which the weak singular kernel is involved with both the unknown and known functions. The regularity and existence of its solution is studied. The collocation methods on discontinuous piecewise polynomial space are considered. The convergence and superconvergence properties of the introduced methods are derived on graded meshes. Numerical results provided to show that our theoretical convergence bounds are often sharp and the introduced methods are efficient. Some comparisons and applications are discussed.

An analytic approach for optimal coordination of overcurrent relays

Abstract: This study presents a new analytic approach to optimal coordination of directional overcurrent relays. This approach is based on the selection of optimum pickup current and time dial setting, in order to obtain minimum operating time for the relays, while satisfying various coordination and boundary constraints. Based on the new optimal relay setting procedure, an iterative numerical solution is proposed. The proposed numerical algorithm converges to the global optimum values, which are independent of initial values and the order of relay setting. The proposed method is applied to three different test systems. The new method is compared with some previously proposed analytic and evolutionary approaches. The results demonstrate the advantages of the proposed method over the previous works.