TY - JOUR
T1 - New aspects of Caputo-Fabrizio fractional derivative
AU - Al-Refai, Mohammed
AU - Pal, Kamal
N1 - Funding Information:
The authors acknowledge the support of the United Arab emirates University under the Fund No. 31S239-UPAR(1) 2016.
Publisher Copyright:
© 2019 NSP.
PY - 2019
Y1 - 2019
N2 - In this paper, we consider classes of linear and nonlinear fractional differential equations involving the Caputo-Fabrizio fractional derivative of non-singular kernel. We transform the fractional problems to equivalent initial value problems with integer derivatives. We illustrate the obtained results by presenting two mathematical models of fractional differential equations and their equivalent initial value problems. We show that it is impossible to convert all types of linear fractional differential equations to the integer ones.The obtained results will lead to better understanding of fractional models, as the solutions of their equivalent models can be studied analytically and numerically using well-known techniques of differential equations.
AB - In this paper, we consider classes of linear and nonlinear fractional differential equations involving the Caputo-Fabrizio fractional derivative of non-singular kernel. We transform the fractional problems to equivalent initial value problems with integer derivatives. We illustrate the obtained results by presenting two mathematical models of fractional differential equations and their equivalent initial value problems. We show that it is impossible to convert all types of linear fractional differential equations to the integer ones.The obtained results will lead to better understanding of fractional models, as the solutions of their equivalent models can be studied analytically and numerically using well-known techniques of differential equations.
KW - Caputo-Fabrizio fractional operator
KW - Fractional differential equations
KW - Initial value problems
UR - http://www.scopus.com/inward/record.url?scp=85071375948&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85071375948&partnerID=8YFLogxK
U2 - 10.18576/PFDA/050206
DO - 10.18576/PFDA/050206
M3 - Article
AN - SCOPUS:85071375948
SN - 2356-9336
VL - 5
SP - 157
EP - 166
JO - Progress in Fractional Differentiation and Applications
JF - Progress in Fractional Differentiation and Applications
IS - 2
ER -