Authors: Atanacković, Teodor
Janev, Marko 
Pilipović, Stevan
Title: Non-linear boundary value problems involving Caputo derivatives of complex fractional order
Journal: Applied Mathematics and Computation
Volume: 334
First page: 326
Last page: 342
Issue Date: 1-Oct-2018
Rank: M21a
ISSN: 0096-3003
DOI: 10.1016/j.amc.2018.04.026
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.
Keywords: Expansions formula for fractional derivatives | Fractional derivative of complex-order | Non-linear fractional boundary value problem
Publisher: Elsevier
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
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