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

Abstract

© 2018 Elsevier Inc. We study approximate solutions of CD tβ y(t)=f(t,y(t)), separately, for β ∈ (0, 1) and β ∈ (1, 2) with different boundary data, where CD tβ 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.