In this article, a new analytic technique based on Parker-Sochacki iteration is introduced for computing series solution of a general nonlinear two-point boundary value problems with Dirichlet and Neumann boundary conditions. For problems with or without analytic solution, we found out that this easy-to-implement method produced highly accurate results without linearization when compared with their closed form solutions.
In this paper, a fractional sub-equation method is proposed for finding exact solutions of the space–time fractional Burger’s equation and the space-time fractional fifth-order Sawda-Kotera equation. The derivative is defined in the Jumarie’s modified Riemann-Liouville sense. The proposed method is based on fractional Riccati’s equation. Accordingly, it was obtained three different exact solutions, namely the generalized hyperbolic function solutions, generalized trigonometric function solutions and rational solutions. The proposed scheme can also be applied to other nonlinear fractional partial differential equations.
In , C. Park generalized the notion of the quasi-normed space, i.e. he introduced the notion of the quasi 2-normed space. He proved several properties of the quasi 2-norm. In , M. Kir and M. Acikgoz gave the procedure of completing the quasi 2-normed space. Several inequalities relating the quasi 2-normed spaces are given in [3,4,5]. Later, in , some properties of the convergent sequences in quasi 2-normed spaces are proven. In this paper, we will introduce the quasi 2-norm of the space Lp (μ), 0<p<1 and we will prove several inequalities relating the quasi 2-norm of this space.
In the present paper, we consider relationships between the basic solution concepts of set-valued optimization, the properties of continuous multifunctions with compact and convex values and the existence of efficient continuous selections using the Maximum Theorem and the Distance method. We also discuss two solution concepts in set-valued optimization problem and prove existence of two types of efficient continuous selections which correspond to the two set-valued optimization solutions, respectively.
In a Boolean ring, every element is trivially multiplicatively generated by idempotent elements. In this paper, we study the structure of rings in which certain subsets are multiplicatively generated by idempotents or multiplicatively generated by idempotents and nilpotents.
This paper focuses on derivation of three-step block method through collocation and interpolation technique with Chebyshev polynomial as basis function. The procedure yields uniform order finite difference formulae for the solution of second order Initial Value Problems in Ordinary Differential Equations. The analysis of the self-starting method shows that the method is efficient, consistent, zero-stable and, hence convergent. The method is more accurate when compared with existing methods.
In the manuscript, a concept of a mixed monotone mapping is acquainted and a coupled fixed point theorems is substantiated for such nonlinear shrinkage mappings in partially ordered exact rectangular metric spaces. We enlarge and universalize the conclusions of these theory.