Variational approach for the fractional exothermic reactions model with constant heat source in porous medium

Abstract

In this paper, a new fractional exothermic reactions model with constant heat source in porous media considering the memory effect is proposed. Applying the fractional complex transform, the fractional model is converted into its partner. Then the variational principle of the problem is successfully established. Based on the obtained variational principle, the Ritz method is used to seek the solution of the fractional model. Finally, the correctness and effectiveness of the proposed method are illustrated by the numerical results with the aid of the MATLAB. The obtained results show that the proposed method is easy but effective, and is expected to shed a bright light on practical applications of fractional calculus.