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

Abstract

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 it 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) ε1, energy resource supply (ERS) ε2, energy resource import (ESI) ε3 and renewable energy resources (RER) ε4. Also, applying the obtained numerical results, we can forecast the rate of these functions for spacial interval of time.

Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection

“…Table 2 shows the residual errors based on the FPA forh = −1 and m = 5, 10. In Table 3, the numerical results are based on the FPA and the termination criterion (1). Thus, we need to have the value ε.…”

“…Modeling different phenomena, solving the model by efficient methods and also control and adjust their parameters are one of the important topics of bio-mathematics which have direct relation with human life. Thus, many mathematicians have been focused on various mathematical models such as energy supply-demand model [1], SIR epidemic model [2], HIV infection [3][4][5], model of smoking habit [6], bovine babesiosis disease [7], model of computer viruses [8][9][10] and many other models. Malaria is one of the important infections for which various models have been proposed to control, prevent and transmit.…”

A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

“…In [11], a fractional order model of HIV infection was discussed, in [12] the application of the Atangana-Baleanu fractional derivative in mathematical biology was studied and in [13], a fractional order HIV model with Caputo and constant proportional Caputo operators was illustrated. An application of the Caputo-Fabrizio fractional derivative to solve a fractional order model of an energy supply-demand system can be found in [14]. For other applications of the fractional order models and also their usual forms please see [15][16][17][18][19][20].…”

Qualitative Analyses of Integro-Fractional Differential Equations with Caputo Derivatives and Retardations via the Lyapunov–Razumikhin Method

“…It should be noted that the Caputo derivative is applicable to continuously differentiable quadratic Lyapunov functions to study qualitative properties of solutions of fractional differential equations and fractional delay differential equations, etc. (see, for example, [25,26,[31][32][33][34][35][36][37]).…”