Open AccessDifferential equations of arbitrary order under Caputo-Fabrizio derivative: some existence results and study of stability
Author(s) -
Kadda Maazouz,
Rosana RodríguezLópez
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022291
Subject(s) - mathematics , uniqueness , contraction mapping , stability (learning theory) , differential equation , contraction principle , fixed point , mathematical analysis , derivative (finance) , simple (philosophy) , fixed point theorem , equilibrium point , computer science , machine learning , philosophy , epistemology , financial economics , economics
In this work, we consider the problem of the existence and uniqueness of solution, and also the simple existence of solution, for implicit differential equations of arbitrary order involving Caputo-Fabrizio derivative. The main tools for this study are contraction mapping principle and Schaefer's fixed point result. We also study the stability of the equations in the sense of Ulam-Hyers and also from the perspective of Ulam-Hyers-Rassias.