Search

In this paper, we will introduce the reconstruction of variational iteration method (RVIM) to solve multi-order fractional differential equations (M-FDEs), which include linear and nonlinear ones. We will easily obtain approximate analytical solutions of M-FDEs by means of the RVIM based on the properties of fractional calculus. Moreover, the convergence of proposed method will be shown. Our scheme has been constructed for the fully general set of M-FDEs without any special assumptions, and is easy to implement numerically. Therefore, our method is more practical and helpful for solving a broad class of M-FDEs. Numerical results are carried out to confirm the accuracy and efficiency of proposed method. Several numerical examples are presented in the format of table and graphs to make comparison with the results that previously obtained by some other well known methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove the convergence of a numerical algorithm that switches in some deterministic or random manner, the control parameter of a class of continuous-time nonlinear systems while the underlying initial value problem is numerically integrated. The numerically obtained attractor is a good approximation of the attractor obtained when the control parameter is replaced with the average of the switched values. In this way, a generalization of Parrondo’s paradox can be obtained. As an application, the Lorenz and Rabinovich–Fabrikant systems are used for illustration. [Copyright &y& Elsevier]

Abstract: In this paper, we consider and study a class of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators in Hilbert spaces. We also construct a new perturbed iterative algorithm framework with errors and investigate variational graph convergence analysis for this algorithm framework in the context of solving the nonlinear operator inclusion couple along with some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. The obtained results improve and generalize some well known results in recent literatures. [Copyright &y& Elsevier]