Application of Variational Iteration Method to Fractional Hyperbolic Partial Differential Equations

Abstract

The solution of the fractional hyperbolic partial differential equation is obtained by means of the variational iteration method. Our numerical results are compared with those obtained by the modified Gauss elimination method. Our results reveal that the technique introduced here is very effective, convenient, and quite accurate to one-dimensional fractional hyperbolic partial differential equations. Application of variational iteration technique to this problem has shown the rapid convergence of the sequence constructed by this method to the exact solution.

High Accuracy Remote Data Detection Method for Underground Space Information Based on Fractional-order Differential Algorithm

“…In recent years, many experts and scholars have studied the theory of fractional-order calculus and found that it is suitable for the study of signals with undesirable characteristics, such as nonlinearity, non-causality, and non-stationarity, and for various data applications. Various research results have been used to solve technical problems in the study of temperature field distributions, image processing, mechanical analysis, and detection technology [34][35][36][37][38]. For example, WANG Bao et al [39] applied fractional partial derivatives to the thickness design of high-temperature protective clothing under limited conditions.…”

Second Order Equations in Functional Spaces: Qualitative and Discrete Well-Posedness

“…Section 7.6 is devoted to fractional hyperbolic differential and difference equations. It is based on results of [94][95][96][97]. Finally, Section 7.7 is devoted to singular perturbation hyperbolic problems.…”

“…In [95,97], the numerical and analytic solutions of the mixed problem for multidimensional fractional hyperbolic partial differential equations with the Neumann condition were presented. The stable difference scheme for the numerical solution of the mixed problem for the multidimensional fractional hyperbolic equation with the Neumann condition was presented.…”

Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order

“…The variational iteration method (VIM) was proposed by He [13][14][15][16] due to its flexibility and convergence and efficiently works with different types of linear and nonlinear partial differential equations of fractional order and gives approximate analytical solution for all these types of equations without linearization or discretization; many author have been studying it; for example, see [17][18][19][20][21]. In this paper, we discuss the VIM for solving FSPDEs and obtain the convergence results of this method.…”