Fractional Partial Differential Equations – A Study by Numerical Methods
Journal Title: International Journal of Mathematics and Computer Applications Research (IJMCAR) - Year 2017, Vol 7, Issue 4
Abstract
This paper is to prove that, the fractional partial differential equation forms a finite domain with the numerical solution by using different fractional derivatives. The two fractions are used to prove the fractional diffusion equation and the fractional dispersion equation. The Fractional Differential Equation is formed from the standard diffusion equation replacing the order, as a second space derivative, with the fractional derivative . The analytical solutions of, both the fractional diffusion equation and dispersion equation were derived. From these three numerical methods, the L1/L2-approximation method, the standard method, and the matrix transform method; only the third method is used to deal with the fractional derivative. The two fractional methods transmute into a system of ordinary differential equations that solves by the graphical method. It concludes by the numerical results, that have demonstrated the three numerical method’s effectiveness and convergence
Authors and Affiliations
Babu .
Keywords
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