In this paper, nonlinear integral equations have been solved numerically by using B-spline wavelet method and Variational Iteration Method (VIM). Compactly supported semi-orthogonal linear B-spline scaling and wavelet functions together with their dual functions are applied to approximate the solutions of nonlinear Fredholm integral equations of second kind. Comparisons are made between the var...

The present study is concerned with studying the dynamical behavior of two space-dimensional nonlinear time-fractional models governing unsteady-flow polytropic-gas (in brief, pGas) that occurred in cosmology and astronomy. For this purpose, efficient hybrid methods so-called optimal homotopy analysis J-transform method (OHAJTM) J-variational iteration transform (J-VITM) have been adopted. OHAJ...

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which ten...

In this paper, we study the existence of infinitely many weak solutions to a fractional Kirchhoff-Schr\"{o}dinger-Poisson system involving singularity, i.e. when $0<\gamma<1$. Further, obtain solution with strong $\gamma>1$. We employ variational techniques prove and multiplicity results. Moreover, $L^{\infty}$ estimate is obtained by using Moser iteration method.

In recent years, it has been found that derivatives of non-integer order are very effective for the description of many physical phenomena such as rheology, damping laws, and diffusion processes. These findings invoked the growing interest on studies of the fractal calculus in various fields such as physics, chemistry, and engineering [1 – 4]. In general, there exists no method that yields an e...

    In this paper, a variational iteration method (VIM), which is a well-known method for solving nonlinear equations, has been employed to solve an inverse parabolic partial differential equation. Inverse problems in partial differential equations can be used to model many real problems in engineering and other physical sciences. The VIM is to construct correction functional using general Lagr...

In this paper a modification of He's variational iteration method (VIM) has been employed to solve Dung and Riccati equations. Sometimes, it is not easy or even impossible, to obtain the first few iterations of VIM, therefore, we suggest to approximate the integrand by using suitable expansions such as Taylor or Chebyshev expansions.

In this paper we present approximate analytical solution of a time-fractional Zakharov-Kuznetsov equation via the fractional iteration method. The fractional derivatives are described in the Caputo sense. The approximate results show that the fractional iteration method is a very efficient technique to handle fractional partial differential equations.