Fractional differential equations have recently demonstrated their importance in a variety of fields, including medicine and applied sciences. The goal of this study is to propose a method based on Physics Informed Neural Network (PINN) for solving differential equations of Caputo fractional order. The proposed method allows to use the knowledge about dynamic of the considered system (governing equation, conservation of energy,...) while exploiting the power of neural networks to solve differential equations and learn the underlying physics of such a system. First, we define a global framework for representing a system of differential equations and how classical PINN’s algorithm works. Then we explain two modifications of this classical algorithm. Next, in order to validate our approach, we showcase the method in various models including the non-linear Van Der Pol oscillation system. Further, we consider problem of blood glucose dynamic for type 1 diabetes using fractional differential equations to model the glucose-insulin metabolism in order to observe the memory effects and gain more insights about the dynamics of system. This model is obtained by considering an adjustment of a modified minimal model of Bergman by converting the model into fractional order model by fitting the fractional order Caputo differential operator in this modified Bergman model. The treatment of type 1 diabetes is based on subcutaneous insulin injections to compensate for declining insulin production by the pancreas. Some preliminary numerical simulations are performed to illustrate the effect of fractional order derivative approach and behavior of model solutions. Lastly, the conclusion and future perspectives are presented.