Analysis of non-homogeneous heat model with new trend of derivative with fractional order

The model of nonlinear heat was generalized using the new trend of derivative with fractional order. The new definition of derivative with fractional order has no singular kernel thus allows a description of the variation on time or space from the lower to the upper boundaries within the space/time interval which the investigation is taken place for a given model. In detail, we presented the analysis of unique and existence of a solution for the nonlinear fractional equation. We present the derivation of a special solution using an iterative method.