Abstract
Recently, Atangana and Baleanu introduced a novel derivative with fractional order with no singular and non-local kernel based on the Mittag-Leffler function. The new derivative is able to portray material heterogeneities and some structure or media with different scales. The non-locality of the new kernel allows better description of the memory within structure and media with different scales. To explicitly explain the reaction-diffusion within an alloy with different elements says, for instance, FeNi and NiFe, we make use of the newly defined fractional operator to enhance this model. We presented the special solution to the new model and some numerical simulations to appreciate the efficacy of the new derivative with fractional order.