An Analytical Technique, Based on Natural Transform to Solve Fractional-Order Parabolic Equations

This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations.

Automated summary

This research article explores the solution of fractional-order parabolic equations using the Adomian decomposition method and natural transform, providing simple and attractive closed form solutions. The obtained results are found to be in good agreement with exact solutions, with convergence observed between fractional and integer-order problem solutions. The technique is considered accurate and can be applied to solve other fractional-order partial differential equations.