Complex variable approach to analysis of a fractional differential equation in the real line

2017/06/27 by Müfit Şan, Şan, Müfit
Mathematics · #30A10 #30C45 #30C80 #32A10 #37C25 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30A10 #msc:30C45 #msc:30C80 #msc:32A10 #msc:37C25

paper · pdf · doi:10.48550/arxiv.1706.08916

14 pages

arxiv created 2017/06/27 · arxiv updated 2017/11/09

Abstract

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: \begincases D^qu(x) = f(x,u(x)),
u(0)=b, (b≠ 0).
\endcases Moreover, in the special cases of considered problem, we investigate some geometric properties of the solutions.

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