The Solutions of Caputo-Fabrizio Random Fractional Ordinary Differential Equations by Aboodh Transform Method

Authors : Yasin Şahin, Mehmet Merdan

Pages : 149-170

Doi:10.18185/erzifbed.1543499

View : 25 | Download : 24

Publication Date : 2025-03-28

Article Type : Research Paper

Abstract :The primary objective of the paper is to employ the Aboodh transformation to solve Caputo-Fabrizio ordinary fractional differential equations. Furthermore, the methodology described is used to solve some common fractional differential equations. Analyzed using the Aboodh Transformation Method are random ordinary differential equations derived by randomly picking the coefficients or initial conditions of Caputo-Fabrizio fractional ordinary differential equations. The initial conditions or coefficients of the equations are converted into random variables distributed according to Normal, Uniform, and Exponential distributions. The probability characteristics, including expected value, variance, coefficient of variation, and confidence interval, of the random ordinary differential equations solved are computed using the MATLAB (2013a) package software. The acquired results are then shown and discussed.
Keywords : Caputo-Fabrizio fractional derivative, Aboodh Transform Method, Continuous probability distributions, variance