A mean-value Approach to solve fractional differential and integral equations

Angelis, Paolo De; Marchis, Roberto De; Martire, Antonio Luciano; Oliva, Immacolata

doi:10.1016/j.chaos.2020.109895

Cited by 8 publications

(1 citation statement)

References 22 publications

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“…Furthermore, solving fractional integrals and equations are among interesting problems. Angelis et al [30] discussed the mean-value approach to solve fractional differential and integral equations, Odibat [31] presented the approximations of fractional integrals and Caputo fractional derivatives and Jahanshahi et al [32] applied the fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives. Also, Suleman [33] applied the Elzaki projected differential transform method for fractional order system of linear and nonlinear fractional partial differential equation.…”

Section: Introductionmentioning

confidence: 99%

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

Noeiaghdam¹,

Sidorov²

2020

MMEP

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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.

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