TY - JOUR
T1 - An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative
AU - Marasi, H. R.
AU - Joujehi, A. Soltani
AU - Aydi, H.
N1 - Publisher Copyright:
© 2021 H. R. Marasi et al.
PY - 2021
Y1 - 2021
N2 - In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution.
AB - In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution.
UR - http://www.scopus.com/inward/record.url?scp=85103660316&partnerID=8YFLogxK
U2 - 10.1155/2021/6624861
DO - 10.1155/2021/6624861
M3 - Article
AN - SCOPUS:85103660316
SN - 2314-8896
VL - 2021
JO - Journal of Function Spaces
JF - Journal of Function Spaces
M1 - 6624861
ER -