In this article we prove existence and uniqueness of global solution to an initial value problem for a nonlinear fractional differential equation with a Caputo–Fabrizio (CF) derivative. We provide a new compact formula for the computation of the CF derivative to power functions (which is given in terms of Mittag–Leffler functions). We also give the convergence to classical derivatives for a regular class of functions when the order of the CF derivative tends to one, as well as some other useful properties.
Digital Object Identifier (DOI)
D. Roscani, Sabrina; Venturato, Lucas; and A. Tarzia, Domingo
"Global Solution to a Nonlinear Fractional Differential Equation for the Caputo–Fabrizio Derivative,"
Progress in Fractional Differentiation & Applications: Vol. 5:
4, Article 2.
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol5/iss4/2