title: Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
abstract: We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
authors.affiliation: Department of Applied Mathematics, Maharaja Agrasen Institute of Technology, Rohini, Delhi 110086, India.
authors.forename: Vipul K
authors.initials: VK
authors.lastname: Baranwal
authors.affiliation: Department of Mathematics and Statistics, Dr. Hari Singh Gaur University, Sagar 470003, India.
authors.forename: Ram K
authors.initials: RK
authors.lastname: Pandey
authors.affiliation: Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi 221005, India.
authors.forename: Om P
authors.identifier: 0000-0003-3391-6392
authors.initials: OP
authors.lastname: Singh