The extended fractional Caputo-Fabrizio derivative of order 0 <= sigma < 1 on C-R[0,1] and the existence of solutions for two higher-order series-type differential equations

Abstract

We extend the fractional Caputo-Fabrizio derivative of order 0 <= sigma < 1 on C-R[0,1] and investigate two higher-order series-type fractional differential equations involving the extended derivation. Also, we provide an example to illustrate one of the main results.