Article Traveling Wave Solutions of Seventh-order Generalized KdV Equations Using He's Polynomials was published on February 1, 2009 in the journal International Journal Nonlinear Sciences and Numerical Simulation (volume 10, issue 2).

We apply the homotopy perturbation method for solving fourth-order boundary value problems. The analytical results of problems have been obtained in terms convergent series with easily computable components. Several examples are given to illustrate efficiency and implementation method. Comparisons made confirm reliability Homotopy can be considered an alternative Adomian decomposition its variant forms.

This paper outlines a detailed study of some relatively new techniques which are originated by He for solving diversified nonlinear problems physical nature. In particular, we will focus on the variational iteration method (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion method, exp‐function method. These but very reliable proved useful wide class capable to cope with versatility problems. Several examples given reconfirm efficiency these algorithms. Some open...

Article Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials was published on June 1, 2008 in the journal International Journal of Sciences and Numerical Simulation (volume 9, issue 2).

Abstract We apply a relatively new technique which is called the homotopy perturbation method (HPM) for solving linear and nonlinear partial differential equations. The suggested algorithm quite efficient practically well suited use in these problems. proposed iterative scheme finds solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify reliability efficiency of method. fact that HPM solves problems using Adomian’s polynomials can...

In this article, we define a new fractional technique which is known as generalized proportional (GPF) integral in the sense of another function Ψ . The authors prove several inequalities for newly defined GPF-integral with respect to Our consequences will give noted outcomes suitable variation and proportionality index ς Furthermore, present application novel operator inequalities. A few properties are exhibited, numerical approximation these operators introduced certain utilities...

The objective of this paper is to obtain some Hermite-Hadamard type inequalities for h-preinvex functions. Firstly, a new kind generalized h-convex functions, termed introduced through relaxing the concept h-convexity by Varosanec. Some functions are established under certain conditions. Our results can be viewed as generalization several previously known results. Results proved in may stimulate further research different areas pure and applied sciences.

Abstract In the article, we introduce a class of n -polynomial harmonically convex functions, establish their several new Hermite–Hadamard type inequalities which are generalizations and variants previously known results for functions.

The investigation of the proposed methods is effective and convenient for solving integrodifferential difference equations. In this note, we introduce generalized $\mathcal{K}$-fractional integral in terms a new parameter $\mathcal{K}>0$ exponentially convex functions. This paper offers some novel inequalities Ostrowski-type using integral. application viewpoint, proved several corollaries that investigate proving Hermite-Hadamard operator. Some numerical examples are offered to explain...

The main objective of this article is to establish some new fractional refinements Hermite–Hadamard-type inequalities essentially using new<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-Riemann–Liouville integrals, where<mml:math id="M3"><mml:mrow><mml:mi>k</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>. Using integral,...

Abstract It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study wide class of unrelated problems, which arise in pure applied sciences. In this paper, we present number new numerical techniques for solving equilibrium problems using various including projection, Wiener-Hopf equations, dynamical systems, the auxiliary principle penalty function. General variational-like are introduced investigated. Properties higher order...

Abstract In this paper, we introduce the non-convex interval-valued functions for fuzzy-interval-valued functions, which are called "Equation missing"<!-- image only, no MathML or LaTex -->-convex by means of fuzzy order relation. This relation is defined level-wise through Kulisch–Miranker given on interval space. By using -->-convexity concept, present fuzzy-interval Hermite–Hadamard inequalities functions. Several exceptional cases debated, can be viewed as useful applications....

-preinvex fuzzy-interval-valued functions Hermite-Hadamard inequalities A B S T R C TIt is well known that convexity and nonconvexity develop a strong relationship with different types of integral inequalities.Due to the importance concept inequality, in this paper, we present some new classes preinvex involving two arbitrary auxiliary asWith help these classes, derive (HH-inequalities) by means fuzzy order relation on fuzzy-interval space verify support nontrivial examples.This defined...