This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the ( G′ G ) -expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic so...

The main aim of this paper is to discuss about, Chebyshev wavelets based approximation solution for linear and non-linear differential equations arising in science and engineering. The basic idea of this method is to obtain the approximate solution of a differential equation in a series of Cheybyshev wavelets. For this purpose, operational matrix for Cheybyshev wavelets is derived. By applying ...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

Abstract. This paper concerns the asymptotic behaviour of solutions of functional differential equations with unbounded delay to non–equilibrium limits. The underlying deterministic equation is presumed to be a linear Volterra integro–differential equation whose solution tends to a non–trivial limit. We show when the noise perturbation is bounded by a non–autonomous linear functional with a squ...

‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...