摘要：The purpose of this paper is to investigate the existence of solutions to the following initial value problem for nonlinear fractional differential equation involving Caputo sequential fractional derivative , , , , where , are Caputo fractional derivatives, , , , and . Local existence of solutions is established by employing Schauder fixed point theorem. Then a growth condition imposed to guarantees not only the global existence of solutions on the interval , but also the fact that the intervals of existence of solutions with any fixed initial value can be extended to . Three illustrative examples are also presented. Existence results for initial value problems of ordinary differential equations with -Laplacian on the half-axis follow as a special case of our results.
