Search

In this paper, a meshless pseudospectral method is applied to solve problems possessing weak discontinuities on interfaces. To discretize a differential problem, a global interpolation by radial basis functions is used with the collocation procedure. This leads to obtaining the differentiation matrix for the global approximation of the differential operator from the analyzed equation. Using this matrix, the discretization of the problem is straightforward. To deal with the differential equations with discontinuous coefficients on the interface, the meshless pseudospectral formulation is used with the so-called subdo-main approach, where proper continuity conditions are used to obtain accurate results. In the present paper, the differentiation matrix for this method is derived and the choice of a proper value of the shape parameter for radial functions in the context of the subdo-main approach is studied. The numerical tests show the effectiveness of the method when using regular or unstructured node distribution. They confirm that the approach preserves well-known advantages of the radial basis function collocation method, i.e., rapid convergence, simplicity of the implementation and extends its usage for problems with weak discontinuity. [ABSTRACT FROM AUTHOR]

In this paper, the standard collocation approach is used to solve multi-order fractional integro-differential equations using Caputo sense. We obtain the integral form of the problem and transform it into a system of linear alge- braic equations using standard collocation points. The algebraic equations are then solved using the matrix inversion method. By substituting the algebraic equation solutions into the approximate solution, the numerical result is obtained. We establish the method’s uniqueness as well as the convergence of the method. Numerical examples show that the developed method is efficient in problem-solving and competes favorably with the existing method. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mathematics, Mechanics & Computer Science is the property of Al-Farabi Kazakh National University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, circuit implementation and anti-synchronization are studied in coupled nonidentical fractional-order chaotic systems where a fractance module is introduced to approximate the fractional derivative. Based on the open-plus-closed-loop control, a nonlinear coupling strategy is designed to realize the anti-synchronization in the fractional-order Rucklidge chaotic systems and proved by the stability theory of fractional-order differential equations. In addition, using the frequency-domain approximation and circuit theory in the Laplace domain, the corresponding electronic circuit experiments are performed for both uncoupled and coupled fractional-order Rucklidge systems. Finally, our circuit implementation including the fractance module may provide an effective method for generating chaotic encrypted signals, which could be applied to secure communication and data encryption. [ABSTRACT FROM AUTHOR]

In this paper, we aim to prove the existence, uniqueness of the solution to the random delay differential equation of fractional order involving the successive approximation method. Moreover, using the Gronwall inequality, we study the continuous dependence of solution in the mean square sense of the problem. Finally, the fractional ϵ-approximate solution in the mean square sense is also considered. [ABSTRACT FROM AUTHOR]

In the theory of uncertainty and approximation neutrosophy plays a significant role. Neutrosophy is tool emerged on standard or non-standard to measured the mathematical model of uncertainty, vagueness, ambiguity etc. In light of these major issues, the paper outlines of Neutrosophic Set, Single Valued Neutrosophic Set, Triangular Single Valued Neutrosophic Number and Trapezoidal Single Valued Neutrosophic Number. It also propose Neutrosophic Differential Equation and shown its solution in different conditions. Thereafter mining safety model via Single Valued neutrosophic number be epitomized. At last a mathematical experiment is done to exhibit its reality and use fullness of this Number. [ABSTRACT FROM AUTHOR]

This article presents a novel numerical approach to the solution of the nonlinear Kawahara equation. The desired approximations are obtained from the combination of Dickson polynomials and Taylor's expansion. The combined approach is based on Taylor's expansion for discretizing the time derivative and Dickson polynomials for space derivatives. The problem will be converted into a system of linear algebraic equations for each time step via some suitable collocation points. Error estimation is presented after obtaining the approximate solution. The newly proposed technique is compared with some existing numerical methods to show the method's applicability, accuracy, and efficacy. Two problems are solved to demonstrate the method's power and effect, and the results are presented as a table and graphics. [ABSTRACT FROM AUTHOR]

Approximate solutions for a family of nonlinear fractional-order differential equations are introduced in this work. The fractional-order operator of the derivative are provided in the Caputo sense. The third-kind Chebyshev polynomials are discussed briefly, then operational matrices of fractional and integer-order derivatives for third-kind Chebyshev polynomials are constructed. These obtained matrices are a critical component of the proposed strategy. The created matrices are used in the context of approximation theory to solve the stated problem. The fundamental advantage of this method is that it converts the nonlinear fractional-order problem into a system of algebraic equations that can be numerically solved. The error bound for the suggested technique is computed, and numerical experiments are presented to verify and support the accuracy and efficiency of the proposed method for solving the class of nonlinear multi-term fractional-order differential equations. [ABSTRACT FROM AUTHOR]

In the current study, a new numerical algorithm is presented to solve a class of nonlinear fractional integral-differential equations with weakly singular kernels. Cubic hat functions (CHFs) and their properties are introduced for the first time. A new fractional-order operational matrix of integration via CHFs is presented. Utilizing the operational matrices of CHFs, the main problem is transformed into a number of trivariate polynomial equations. Error analysis and the convergence of the proposed method are evaluated, and the convergence rate is addressed. Ultimately, three examples are provided to illustrate the precision and capabilities of this algorithm. The numerical results are presented in some tables and figures. [ABSTRACT FROM AUTHOR]

In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations of each solution in terms of a formal power series. Some numerical approximations are implemented by using truncated series. [ABSTRACT FROM AUTHOR]

A method for constructing finite-dimensional approximations for the optimal impulse stabilizing control of a linear autonomous system of differential equations with aftereffect is proposed. Auxiliary finite-dimensional problems of optimal stabilization of linear autonomous systems of ordinary differential equations with non-impulse controls are used. A procedure for reducing the dimension of a system of algebraic matrix Riccati equations is described. [ABSTRACT FROM AUTHOR]