Approximate analytical solution of 3D fractional microscale heat equation using modified homotopy perturbation method

Abstract

In the present article, we use modified homotopy perturbation method (HPM) to find approximate analytical solution of three-dimensional time fractional microscale heat transport equation. This transport equation is at first converted into the equation of two functions. First one have both, the first order fractional time derivative and second order space derivatives, while second one has only second order space derivative. Then applying modified HPM on first function and corresponding increment in second function obtain by Taylor's expansion for equal time step homotopically and for solution, couples them. Obtained solution is compared with the previous numerical result for integer order time derivative [2]. It is found that the procedure is easy and user friendly in comparison to previous work.