in this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the hunter-saxton equation. the main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. it is a semi analytical-numerical metho...

The present paper introduces a new class of bi-univalent functions defined on symmetric domain using Gegenbauer polynomials. For in this class, we have derived the estimates Taylor–Maclaurin coefficients, a2 and a3, Fekete-Szegö functional. Several results follow upon specializing parameters involved our main results.

In this work, we introduce and investigate a new subclass of analytic bi-univalent functions based on subordination conditions between the zero-truncated Poisson distribution Gegenbauer polynomials. More precisely, will estimate first two initial Taylor–Maclaurin coefficients solve Fekete–Szegö functional problem for belonging to subclass.

Abstract In this paper, a new form of the homotopy perturbation method (NHPM) has been adopted for solving integro-differential equations. In the present study, firstly the NHPM is used to the integro-differential equation, which yields the Maclaurin series of the exact solution. By applying the Laplace transformation to the truncated Maclaurin series and then the Padé approximation to the solu...

A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric defined in ?={z?C:|z|<1} is introduced. The estimates for general Taylor–Maclaurin coefficients introduced are obtained by making use Faber polynomial expansions. In particular, several previous results generalized.

Several different subclasses of the bi-univalent function class Σ were introduced and studied by many authors using distribution series like Pascal distribution, Poisson Borel Mittag-Leffler-type Miller–Ross-Type Distribution. In present paper, making use Bell we introduce investigate a new family GΣt(x,p,q,λ,β,γ) normalized functions in open unit disk U, which are associated with Horadam polyn...

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

A method for analysing a class of divergent series is developed from the Euler– Maclaurin summation formula. The conditions that the summand must satisfy are explored, and a significant simplification is obtained for cases where the summation ranges over all integers. As an example, we consider the Ewald representation for Schlömilch series, and show that this includes Twersky’s dual series for...

The papers [15], [16], [4], [12], [2], [14], [5], [1], [3], [7], [6], [10], [11], [8], [9], [17], and [13] provide the notation and terminology for this paper. The following proposition is true (1) For every real number x and for every natural number n holds |x| = |x|. Let f be a partial function from R to R, let Z be a subset of R, and let a be a real number. The functor Maclaurin(f, Z, a) yie...

In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent...