Fractional-Order Investigation of Diffusion Equations via Analytical Approach - Liu, Haobin; Khan, Hassan; Mustafa, Saima; Mou, Lianming; Baleanu, Dumitru (Frontiers in Physics, 2021)
The current research article is mainly concerned with the analytical solution of diffusion equations within Caputo fractional-order derivative. The motivation and novelty of the current work is to apply a sophisticated and straight forward procedure to solve diffusion equations containing derivative of fractional-order. The solutions of some illustrative examples are calculated to confirm the closed contact between the actual and the approximate solutions of the targeted problems. It is analyzed that the proposed solution have the higher rate of convergence and provide the closed form solution. The small number of calculation is the main advantage of the proposed method. Due to an easy and straight forward implementation, the suggested method can be utilized to nonlinear fractional-order problems in various branches of applied science, it can be extended to solve other physical problems of fractional-order in various areas of applied sciences.