Caputo-Fabrizio Fractional Derivative to Solve the Fractional Model of Energy Supply-Demand System.

The aim of this study, is to present the fractional model of energy supply-demand system (ES-DS) based on the Caputo-Fabrizio derivative. For the first time, the existence and uniqueness of solution of the fractional model of ES-DS are proved and t is the main novelty of this paper. Also, we know that the obtained results from mathematical models with fractional order are more accurate than usual models. This model is based on four important functions, energy resources demand (ERD) ei, energy resource supply (ERS) S2, energy resource import (ESI) S3 and renewable energy resources (RER) e4. Also, applying the obtained numerical results, we can forecast the rate of these functions for spacial interval of time. [ABSTRACT FROM AUTHOR]