Non-linear boundary value problems involving Caputo derivatives of complex fractional order

We study approximate solutions of CDtβy(t)=f(t,y(t)), separately, for β ∈ (0, 1) and β ∈ (1, 2) with different boundary data, where CDtβ is the Caputo fractional derivative of complex-order. For this purpose we use the expansion formula for such fractional derivatives and prove the existence and the uniqueness of approximate solutions under certain conditions and their convergence to the original solutions.