Numerical solutions of time fractional degenerate parabolic equations by variational iteration method with Jumarie-modified Riemann-Liouville derivative

作者：Roul Pradip^*

来源：Mathematical Methods in the Applied Sciences, 2011, 34(9): 1025-1035.

DOI：10.1002/mma.1418

• variational iteration method
• biological population equations
• fractional calculus
• exact solution
• Mittag-Leffler function

In this article, the fractional variational iteration method is employed for computing the approximate analytical solutions of degenerate parabolic equations with fractional time derivative. The time-fractional derivatives are described by the use of a new approach, the so-called Jumarie modified Riemann-Liouville derivative, instead in the sense of Caputo. The approximate solutions of our model problem are calculated in the form of convergent series with easily computable components. Moreover, the numerical solution is compared with the exact solution and the quantitative estimate of accuracy is obtained. The results of the study reveal that the proposed method with modified fractional Riemann-Liouville derivatives is efficient, accurate, and convenient for solving the fractional partial differential equations in multi-dimensional spaces without using any linearization, perturbation or restrictive assumptions.

• 出版日期2011-6