Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems

We were concerned with the description of the boundary layers problems within the scope of fractional calculus. However, we will note that one of the main methods used to solve these problems is the matched asymptotic method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the matched asymptotic method to the scope of fractional derivative, we proposed a relatively new derivative called the beta-derivative. We presented some useful information for this operator. With the reward of this operator, we presented the idea of matched asymptotic method in finding solutions of the fractional boundary layers problems. The method was illustrated with an example.