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Research Article Open access CC BY 4.0

Analytical Approximate Solutions of Fractional Convection-Diffusion Equation by Means of Local Fractional Derivative Operators

Mehmet Merdan

Journal of Advances in Mathematics and Computer Science · pp. 1–15 · Published 7 May 2016

10.9734/BJMCS/2016/25827

Abstract

In this article, the local fractional decomposition method (LFDM) is applied to obtain approximate the analytical solution of nonlinear fractional convection-diffusion. Numerical solutions obtained by local fractional decomposition method are compared with the exact solutions, revealing that the obtained solutions are of high accuracy. A new application of local fractional decomposition method (LFDM) was extended to reproduce the analytical solutions to this equation in the form of a series. It is shown that the solutions obtained by the LFDM are reliable, simple and that LFDM is an effective method for strongly nonlinear partial equations.

Local fractional decomposition method fractional convection-diffusion equation Riemann-Liouville derivative.

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