The first aim of this work is to establish a Peano type existence theorem for an initial value problem involving complex fractional derivative and the second is, as a consequence of this theorem, to give a partial answer to the local existence of the continuous solution for the following problem with Riemann-Liouville fractional derivative: \begin{ equation*} \begin{ cases} &D^{ q}u(x) = f\big(x,u(x)\big), \\ &u(0)=b, \ \ \ (b\neq 0). \\ \end{ cases} \end{ equation*} Moreover, in the special cases of considered problem, we investigate some geometric properties of the solutions.
Categories: math.CV