Abstract
Abstract In this article, a modified variational iteration method along with Laplace transformation is used for obtaining the solution of fractional-order nonlinear convection–diffusion equations (CDEs). The proposed technique is applied for the first time to solve fractional-order nonlinear CDEs and attain a series-form solution with the quick rate of convergence. Tabular and graphical representations are presented to confirm the reliability of the suggested technique. The solutions are calculated for fractional as well as for integer orders of the problems. The solution graphs of the solutions at various fractional derivatives are plotted. The accuracy is measured in terms of absolute error. The higher degree of accuracy is observed from the table and figures. It is further investigated that fractional solutions have the convergence behavior toward the solution at integer order. The applicability of the present technique is verified by illustrative examples. The simple and effective procedure of the current technique supports its implementation to solve other nonlinear fractional problems in different areas of applied science.
Highlights
Fractional calculus (FC) is the branch of mathematics which can be used to analyze various problems in science and engineering more accurately as compared to ordinary calculus
Many other problems in applied sciences are modeled by fractional-order partial differential equations (PDEs) [1,2,3]
Convection–diffusion equations (CDEs) of fractional-order are solved by the homotopy perturbation method (HPM) and variational iteration technique along with Laplace transform (VHPTM)
Summary
Fractional calculus (FC) is the branch of mathematics which can be used to analyze various problems in science and engineering more accurately as compared to ordinary calculus. Many other problems in applied sciences are modeled by fractional-order partial differential equations (PDEs) [1,2,3]. Various dynamical systems in physics and engineering are modeled by using fractional-order differential equations. The study of nonlinear PDEs modeling different physical processes has become a significant tool. Convection–diffusion equations (CDEs) of fractional-order are solved by the homotopy perturbation method (HPM) and variational iteration technique along with Laplace transform (VHPTM). VHPTM [34,35,36,37,38,39] is a hybrid technique and carry the beneficial features of both HPM and varational iteration method (VIM) and is very consistent with various physical problems. The proposed technique provides the closed and series-form solution having computable and convergent terms [40]
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