On the existence and uniqueness of solutions of a class of fractional differential equations

In this paper, we investigate the existence and uniqueness of solutions for the following class of multi-order fractional differential equationsDβ1γ1,δ1⋯Dβnγn,δnu(t):=∏i=1nDβiγi,δiu(t):=Dβi,nγi,δiu(t)=f(t,u(t)),t∈[0,1],u(0)=0,∑i=1nδi⩽1,γi>0,βi>0,1⩽i⩽n, where Dβi,nγi,δi denotes the generalized Erdélyi–Kober operator of fractional derivative of order δiδi. Moreover, some properties concerning the positive, maximal, minimal, and continuation of solutions are obtained.