In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. E...

In the present paper, hybrid differential transform and finite difference method (HDTFD) is applied to solve 2D transient nonlinear straight annular fin equation. For the case of linear heat transfer the results are verified with analytical solution. The effect of different parameters on fin temperature distribution is investigated. Effect of time interval of differential transform on the stabi...

Based on high order approximation of L-stable RungeKutta methods for the Riemann-Liouville fractional derivatives, several classes of high order fractional Runge-Kutta methods for solving nonlinear fractional differential equation are constructed. Consistency, convergence and stability analysis of the numerical methods are given. Numerical experiments show that the proposed methods are efficien...

In this paper, we will introduce a method to find a numerical solution of nonlinear age-structured population model using second-kind Chebyshev polynomials. This method convert the nonlinear age-structured population models to an equivalent differential equation. We introduce two variable second-kind Chebyshev polynomials and their basic properties. These properties will be used to reduce the o...

Abstract In this paper, other types of exact solution of a first-order nonlinear ordinary differential equation is further investigated. By using the solutions of this equation, and a new general ansatz, we give some types of solutions of a class of nonlinear partial differential equations and MKdV equation. These solutions includes solitary wave solutions, singulary solitary solitary solutions...

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

In this paper, we investigate a new type of random $F$-contraction and obtain a common random fixed point theorem for a pair of self stochastic mappings in a separable Banach space. The existence of a unique solution for nonlinear fractional random differential equation is proved under suitable conditions.

The authors have developed a Taylor series method for solving numerically an initial-value problem differential algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit, see BIT 45:561–592, 2005 and BIT 41:364-394, 2001. Numerical results have shown this method to be efficient and very accurate, and particularly suitable for problems that are of too high an ...

In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comp...