We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schrödinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our result covers cases where the bifurcation equation is infinitedimensional, such as the nonlinear Schrödinger equation with zero mass, for which solutions which at ...

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space ...

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

in this paper, modified simple equation method has been applied to ob-tain generalized solutions of burgers, huxley equations and combined forms of these equations. the new exact solutions of these equations have been obtained. it has been shown that the proposed method provides a very effective, and powerful mathematical tool for solving nonlinear partial differential equations.

In this study, a numerical solution of singular nonlinear differential equations, stemming from biology and physiology problems, is proposed. The methodology is based on the shifted Chebyshev polynomials operational matrix of derivative and collocation. To assess the accuracy of the method, five numerical problems, such as the human head, Oxygen diffusion and Bessel differential equation, were ...

‎In this paper‎, ‎a spectral Tau method for solving fractional Riccati‎ ‎differential equations is considered‎. ‎This technique describes‎ ‎converting of a given fractional Riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎We use fractional derivatives in the Caputo form‎. ‎Convergence analysis of the proposed method is given an...

In this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (DTM). This is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. Several numerical examples are given and by comparing the numerical results obtained from DTM  and  predi...

A mixture of liquid and gas bubbles of the same size may be considered as an example of a classic nonlinear medium. In practice, analysis of propagation of the pressure waves in a liquid with gas bubbles is important problem. We know that there are solitary and periodic waves in a mixture of a liquid and gas bubbles and these waves can be described by nonlinear partial differential equations. A...

In this paper, the nonlinear differential equation for the convection of the temperature distribution of a straight fin  with the thermal conductivity depends on the temperature is solved using Adomian Decomposition Method and Padé approximation(PADM) for boundary problems. Actual results are then compared with results obtained previously  using digital solution by Runge–Kuttamethod and a diffe...