TY - JOUR
T1 - On solutions of linear and nonlinear fractional differential equations with application to fractional order RC type circuits
AU - AlAhmad, Rami
AU - Al-Khaleel, Mohammad
AU - Almefleh, Hasan
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2024/3/1
Y1 - 2024/3/1
N2 - In this paper, we solve a class of fractional differential equations of order α∈(0,1) in Caputo–Fabrizio sense. Importantly, we highlight relations between the Caputo–Fabrizio and standard first order derivatives that are very important for the understanding of Caputo–Fabrizio theory and how it can be applied. Moreover, using the exactness of differential equations concept, implicit analytical solutions of such equations are presented which are extensions and generalizations to the results found in the literature. Application to fractional order RC type circuits and other examples are given to illustrate the validity and reliability of our results and theory.
AB - In this paper, we solve a class of fractional differential equations of order α∈(0,1) in Caputo–Fabrizio sense. Importantly, we highlight relations between the Caputo–Fabrizio and standard first order derivatives that are very important for the understanding of Caputo–Fabrizio theory and how it can be applied. Moreover, using the exactness of differential equations concept, implicit analytical solutions of such equations are presented which are extensions and generalizations to the results found in the literature. Application to fractional order RC type circuits and other examples are given to illustrate the validity and reliability of our results and theory.
KW - Caputo–Fabrizio theory
KW - Exact differential equations
KW - Fractional calculus
KW - Fractional differential equations
KW - Fractional order RC circuits
UR - http://www.scopus.com/inward/record.url?scp=85175651543&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2023.115507
DO - 10.1016/j.cam.2023.115507
M3 - Article
AN - SCOPUS:85175651543
SN - 0377-0427
VL - 438
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 115507
ER -